Sacred Geometry Calculus of nature
Shravan Pramod Padate Semester IX (Part 1)
Guided by Ar. Mridula Pillai Gudekar
Bachelors of Architecture
L.S. Raheja School of architecture, Mumbai Affiliated to Mumbai University 2021-2022
SACRED GEOMETRY
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DECLARATION I hereby declare that this written submission entitled “Sacred Geometry: Calculus of Nature” represents my ideas in my own words and has not been taken from the work of others (as from books, articles, essays, dissertations, other media and online); and where others’ ideas or words have been included, I have adequately cited and referenced the original sources. Direct quotations from books, journal articles, internet sources, other texts, or any other source whatsoever are acknowledged and the source cited are identified in the dissertation references. No material other than that cited and listed has been used. I have read and know the meaning of plagiarism* and I understand that plagiarism, collusion, and copying are grave and serious offences in the university and accept the consequences should I engage in plagiarism, collusion or copying. I also declare that I have adhered to all principles of academic honesty and integrity and have not misrepresented or fabricated or falsified any idea/data/fact source in my submission. This work, or any part of it, has not been previously submitted by me or any other person for assessment on this or any other course of study.
Signature of the Student: Name of the Student: Shravan Pramod Padate Exam Roll No: Date:
Place:
*The following defines plagiarism: Plagiarism occurs when a student misrepresents, as his/her own work, the work, written or otherwise, of any other person (including another student) or of any institution. Examples of forms of plagiarism include: the verbatim (word for word) copying of another’s work without appropriate and correctly presented acknowledgement; the close paraphrasing of another’s work by simply changing a few words or altering the order of presentation, without appropriate and correctly presented acknowledgement; unacknowledged quotation of phrases from another’s work; the deliberate and detailed presentation of another’s concept as one’s own. Another’s work covers all material, including, for example, written work, diagrams, designs, charts, photographs, musical compositions and pictures, from all sources, including, for example, journals, books, dissertations and essays and online resources.
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CERTIFICATE
This is to certify that Shravan Pramod Padate has successfully completed his/her design dissertation (Part 1) on the topic “Sacred Geometry: Calculus of Nature” under the guidance of Ar. Mridula Pillai Gudekar. The dissertation is undertaken as a part of the academic study based on the curriculum for Bachelors of Architecture program conducted by the University of Mumbai, through L.S. Raheja School of Architecture, Mumbai. SEAT NUMBER: ______
Ar. Mridula Pillai Gudekar Thesis Guide L. S. Raheja School of Architecture, Mumbai
Ar. Mandar Parab Principal L. S. Raheja School of Architecture, Mumbai
External Juror 1:
External Juror 2:
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ACKNOWLEDGEMENT
This past year has made me realize the meaning of ‘It takes a village’. The satisfaction and contentment of successfully completing the thesis would not be truly complete without the mention of the people that made it possible with their constant support, guidance and motivation. First of all, I would like to thank my parents Pramod Padate and Manisha Padate for their unflinching support throughout these years, for being the most positive source of encouragement and entertainment throughout. My elder sister Ar. Shraddha for her continuous guidance and helping me cheer up and being the annoying sibling that she is. A big thank you to Ar. Mridula Pillai Gudekar for the being the best guide and mentor, without whom this thesis wouldn’t have been possible. For her constant support, advice, encouragement, her belief in me and for always pushing me to give my best. Thank you to Ar. Rubel Dhuna for providing a fresh perspective at architecture. All the faculty at L.S. Raheja School of Architecture who were an integral part of my journey – Ar.Anuj Gudekar, Ar. Swanand Mahashabde, Ar. Arun Fizardo, Ar. Mandar Parab, Ar. Meghana Patil, Ar. Anmol Warang, Ar. Rohan Patil, Ar. Parvez Charania, Ar. Krishnan V, Ar. Neeta Sarode - and taught me everything that I know today. A special thanks to Nidhi for being with me through thick and thin, for supporting me in everything that I did, my partner-in-crime. To my boys – Nishant and Sandesh for all the crazy conversations and fun times – thanks for keeping me sane throughout with your antics. The ‘lockdown internship’ with Neha and Nidhi – to all video call worknights and ‘photoshoots’ and sightseeing plans. To Divya and Saket, for being the most entertaining juniors. My Design Team for supporting me throughout this year. My NASA Gang of all 5 years for the teamwork that made us win trophies and to all the sleepless nights in college for the unforgettable memories. My gratitude to anyone else that I have missed out above, without whom this thesis would have been incomplete.
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Harmony of the world is made manifest in form and number and the heart and soul and all the poetry of natural philosophy are embodied in the concept of mathematical beauty." -(D’arcy Wentworth Thompson) Source - www.etsy.com SHRAVAN PADATE/FIFTH YR. B.ARCH
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PREFACE The spontaneous generation of life began after the explosion of the big bang. A physical reality we live in was created by particles of matter by self-replicating and self-assembling or bonding with other matter to embark on the evolution of the world. To maintain the balance in nature, energies of creation organize these particles into forms and shapes. These forms are the simplest and purest geometry that make up all living things in nature and are thus jointly termed as sacred geometry. "What differs sacred geometry from geometry?" Shapes can be recurring patterns, ratios and fractals. It governs the idea of all consciousness, including human consciousness, which helps us understand where we have come, where we are now and where we are going. These patterns are fundamental guidance for the life in the universe that exists all around us. Our entire physical and intellectual world is governed by sacred geometry which is based on a language of numbers and factors. "Mathematics is the alphabet with which God has written the universe."
-(Galileo)
"What makes these patterns and shapes sacred?" The physical reality that we live in was built based on solids that existed thousands of years before their discovery by the Greek philosopher Plato. Hence those solids are known as platonic solids. Those five solids possess unique attributes which make them important aspects of sacred geometry. They contain every possible molecular connection and geometric laws of reality and the universe. Each platonic solid has a connection with one of the elemental energies organized in a specific pattern of creation, they possess life force energy, light, sound, colour. Since ancient times, philosophers and artists have invoked the strength of sacred geometry in their works. The golden ratio or spiral(3rd dimension) has been representing sacred geometry in natural elements from flowers and animals to the proportions of the human body, hidden behind the Fibonacci sequence. The golden ratio is infinite, as there is no beginning or end to it. Fibonacci worked out the sequence of numbers that explain the golden ratio formation in nature to overcome this. This discovery opened the gates of geometry to the construction and architectural world. Since then it has been an integral part of building construction. Sacred geometry has been used in construction since 300 BCE. from the age of megaliths, Greeks and Egyptians to the revolution in renaissance and organic construction of the modern times. These structures are specifically designed based on sacred geometry. "What are the language and principles of sacred geometry and how does it work with architecture?" Sacredness isn’t just related to religious activities, but also related to the atmosphere, arts and a sense of place. Form and the geometry have changed according to the place and the conditions which have a major impact on people. For me, sacred geometry doesn’t just affect visually but is more related to the feel of human consciousness. "How does sacred geometry affect architecture and people around it?" "What are the scientific reasons behind the behaviour of the geometric forms?"
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AIM To study the impact of sacred geometry on Form and Space and its impact on one’s experience of the designed piece of architecture, keeping in mind changes in the environment and in our lifestyles.
Source - www.flickr.com SHRAVAN PADATE/FIFTH YR. B.ARCH
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NEED FOR STUDY Sacred geometry is a spiritual reality of the universe and found in the world around us. It can be found in leaves and branches of trees, Architecture and the human body as well. It has been established as the heart of the tangible and intangible pattern known to us that comes together to create an amalgamation of energy, light and sacred geometry that corelate our physical, emotional, mental and spiritual aspects. The sacred shapes like the flower of life, the seed of life, an egg of life, the fruit of life and the tree of life contain the pattern of creation and these patterns were found in most ancient civilizations. These geometric forms and patterns exist within nature and release energy in the form of vibrations. These vibrations determine the quality of space and how space is going to affect the user. If the built environment is constructed based on these geometric forms with specific orientation and proportion in harmony with the unbuilt environment, can the vibrations thus enhance the quality of the designed space for well being?
OBJECTIVES 1. To understand the difference between geometry and sacred geometry 2. To study the relationship between sacred geometry and architecture. 3. To study forms and patterns that make a space sacred. 4. To understand the language and principles of sacred geometry. 5. To study the system of balance of nature in relation to sacred geometry. 6. To study the harmony of built and unbuilt environments.
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METHODOLOGY UNDERSTANDING THE TERM "SACRED GEOMETRY" AND STUDYING ITS ASPECTS Sacred geometry is known with various uniformities in a different era. It is a fusion of scientific and spiritual identities. Hence it is important to understand how these identities affect the aspects of architecture and bring harmony to them. STUDYING THE PRINCIPLES AND BEHAVIOUR OF SACRED GEOMETRIC FORMS AND PATTERNSSacred geometry is based on forms, shapes and patterns. These forms and patterns are formed by specific lines of proportions, Which determines their properties and principles. STUDYING THE EVOLUTION OF SACRED GEOMETRY WITH TIME Evolution is important for everything in the world. With the change in time, sacred geometry endures its journey from the ancient to the modern era and unrolls in different cultures with various identities by keeping its spirit the same. UNDERSTANDING THE ROLE OF SACRED GEOMETRY AND ITS APPLICATION INARCHITECTUREGeometry has been an intrinsic part of the architecture. The term ‘Sacred’ is not just associated with religious identity but is more related to energies and vibrations. It is important to understand why it is applied and how it affects the architecture. STUDYING VARIOUS STRUCTURES AROUND THE WORLD WHICH ARE DESIGNED BASED ON SACRED GEOMETRY Sacred geometry has been used in construction since 300 BCE. Hence it is most important to study its appearance in different religions and cultures. UNDERSTANDING THE INFLUENCE OF SACRED GEOMETRY ON THE HUMAN BODY AND ITS CONSCIOUSNESS Sacred geometric elements originated in nature and they radiate energy in the form of vibrations, which affect every living thing around it including humans to reach their consciousness. STUDYING THE HARMONY BETWEEN BUILT AND UNBUILT ENVIRONMENTS TO MAINTAIN BALANCE WITH NATURE CONCERNING SACRED GEOMETRY Geometry has emerged in nature but with the change in times and evolution, It has been incorporated in buildings. But it is imperative to understand to maintain the balance between built and unbuilt environment by harmonizing it and how sacred geometry is a part of it.
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"The Sacred is never intentionally chosen. But someway or the other reveals itself." ~ Eliade
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INTRODUCTION Sacred space always existed around us. The idea of sacredness has been comparable with mythology and religion for a long period of time. But with the changing world sacred has been expanded to encompass enomousamounts of thoughts. The sacred is broken down in several categories from religion and secularity, Individualistic and collective, Rational and atmospheric.
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The whole inhabited earth is a sacred space in which God lives, breathes, and acts.” — Carter Heyward
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WHAT IS SACRED?
The sacred shows up in myths, sounds, ritual action, individuals, and natural objects. Through retelling the myth the divine activity that was done "in the beginning" is rehashed. The redundancy of the sacred activity typically copies the structure and control that built up the world initially. Hence, it is critical to know and protect the interminable structure through which man has life, for it is the demonstration and source of control within the present.
The visual representation of sacred (Source - academia.edusoft.ro)
The human kind Is mindful about the existence of sacrosanct since it showed itself, evince itself, as completely distinctive, something which isn’t secular. It could be the heart and soul of the most profound sense of being. Individuals tend to have a distinctive conviction for being sacred. For a few, the sacrosanct is coequal to higher powers or principled creatures and for a few think of it in a broader sense, one that encompasses mountains, music, dreams and virtues. Both the viewpoints of conviction are exact.
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The sacrosanct may be a hypothesis of God, the divine and supernatural reality, as well as viewpoints of life that take on the brilliant character and representation of divinity. The concept of sacrosanct can be pictured as the sacrosanct centre and the sacrosanct ring that circles the core, where the sacrosanct centre depicts the concept of God, higher control and divinity. But the sacrosanct isn’t fair to the concept of awesome reality and divine being. It could be a sacred ring of other aspects of life, in fact sacrosanct themselves, by associating with the core of the sacred.
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Your sacred space is where you can find yourself again and again. - Joseph Campbell The way towards the sacred (Source - blog.spiritualify.com)
Interpretation of sacred: 1. Committed for the veneration of divinity. 2. Faithful to one service or purpose 3. Worthy of religious adoration: holy 4. Entitled to reverence and respect 5. Of or relating to religion: not secular or profane
The thought of sacredness is to figure out the sense of meaning or purpose through divine, nature and extreme reality. Sacredness isn’t as it were related to god or divine beings, to primary world religions, their particular objects of adoration or specific value of these religions. Moreover our ordinary interests can be considered sacrosanct to ourselves as long as we see the numinous quality of these personal quest within the seek for association with the divine, the nature or the extreme.
6. Highly valued and important 7. Devoted and crucial
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Source - www.dailypioneer.com
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SPIRITUALITY Spirituality is a wide term with several interpretations. In general, it involves a sense of connection to something larger than oneself, as well as a desire for purpose in life. As such, it is a universal human experience that affects us all. A spiritual experience might be described as sacred, transcendent, or simply as a profound sensation of aliveness and connection. Spirituality is acknowledging a feeling, sensation, or conviction that there is something larger than me, that there is more to being human than sensory experience, and that the greater total of which we are a part is cosmic or divine in nature. Spirituality entails understanding that our lives have meaning in a context that extends beyond the biological necessities that drive greed and aggressiveness. It entails understanding that we are an important component of the universe’s intentional development of Life. Many people have found peace and relief from stress through spirituality and religious engagement. While individuals utilise a variety of religions and paths to discover God or express their spirituality, research has shown that those who are more religious or spiritual and use their spirituality to cope with life’s problems reap several health and well-being advantages.
Secular, spiritual and religious existential orientations (Source - www.sciencedirect.com)
Spirituality reveals the person’s true purpose in life. If a person is puzzled as to why he was born, spiritual life might provide answers. It also allows him to accept life as it is and forgive himself for his pain. It encourages people to live in peace and harmony. It reduces violence, aggressiveness, and conflict. It promotes acceptance and forgiving, allowing everyone to coexist peacefully. It aids in the correct organisation of society. Spirituality brings mental tranquilly as well as stability in the home and at work. It aids in the development of tolerance and patience. Spirituality broadens and deepens one’s understanding and insight. Spirituality is a way of gaining knowledge from within.It aids man in maintaining control over nature. It’s incredible that we can keep nature under control. Even with our science and technology, we can’t accomplish it.
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SCIENCE AND SPIRITUALITY: TWO SIDES OF COIN OF SACRED Human intellect is instructed to accept that science and spirituality are two considerations which restrict the perspectives of each other. Science and spirituality both point to discovering hidden laws of nature. Science reveals the most profound spiritual truth and spirituality explores the cause behind logical truth. The point is to discover the higher control that made everything to form our lives better. Science demonstrates the presence of control of creation through physical viewpoints whereas spirituality demonstrates the control of creation through awareness.
Relation between science and spirituality Source - www.sciencedirect.com
Science and Spirituality as two sides of the same sacred coin (Source - wallup.net)
Science and Spirituality make an exceptional organization. Within the occasion that those locked in science spend a number of time inside the calm of their selves, inspiration will come and lead them to the answers for which they seek. Essentially, on the off chance that those captivated by spirituality apply the consistent law of testing speculations inside the research facility of their claimed body and soul, they will discover what comes around.
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In order to incorporate the reasoning of exquisite simplicity, we have to understand the relationship between science and spirituality. A few individuals think that science and spirituality are polar contrary energies, but are they? Science is almost things which can be measured, and the most profound sense of being is approximately things which cannot be measured. In life, both of these are coordinates together. See at our bodies. Able to measure the weight, length, width, structure, and anatomy of the body. But we too have intelligence. So spirituality is approximately what cannot be measured. We ought to measure what can be measured, but we too ought to acknowledge the truth
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"The notion that science and spirituality are somehow mutually exclusive does a disservice to both." — Carl Sagan
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WHY IS SACREDNESS IMPORTANT? The concept of sacredness is an important and universal component of human existence. Although the particular content of spiritual belief, practise, and experience differs, all civilizations have a belief in an ultimate, transcendent, or divine power. Scientists generally describe sacredness as the search for or connection with spirituality. This has virtually become a consensus definition among scientists studying holiness. Three fundamental elements are embedded in this definition: the holy or transcendent, a link or relationship with spirituality, and the search for ultimate meaning or purpose. Divine illumination penetrates our conscience and extends beyond our intellect and ego to aid in the attainment of serenity. In the midst of the darkness, a spiritual mind finds bliss. The discontent we feel is overcome by the everlasting calm that we suppress while striving for harmony. Spirituality may cure our minds and relieve us of the vagaries of life in today’s world. Despite advances in technology and information, people in the modern world are increasingly vulnerable to depression and other mental health issues brought on by societal, personal, and economic challenges. The negativity that surrounds us causes a slew of psychological issues that can lead to major diseases and, in some cases, lead to a person’s death. Peace of mind is required for humans to see the value of life and let go of the negativity that clouds our thoughts and prevents us from experiencing the happiness.
Connection between spirituality and consciousness (Source - www.dreamstime.com)
Detoriation of soul and body (Source - www.dreamstime.com)
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Strength of Sacredness (Source - www.dreamstime.com)
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Worship, sacraments, sacrifices, and festivals are all closely related to vocal manifestations of sacred power. Part of the significance of religious ritual is that everything has a place in the world of the sacred. Human existence must be as near to the divine plan as possible in order to thrive. Theological and philosophical interpretations of the significance of sacraments vary among religious traditions.By definition, the sacred penetrates all aspects of existence. However, there is a specific emphasis on time, place (cosmos), and active actors in the religious perception portrayed in divine storey and ritual (heroes, ancestors, divinities). When seen through the dichotomy of sacred and profane—which implies that the sacred is entirely other than, yet vital for, everyday existence—it is critical to understand and engage with the sacred.
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SACRED SPACE 1.6.1 Experience of Sacred Space
Understanding sacred space (Source - www.archdaily.com)
Understanding a sacred space is a bit like meandering under the night sky with a feeling of amazement. We can surely look for the mind boggling scale of astronomic events, our comparative insignificance, the mystery of our presence in the universe, all of which provide feelings which always amazes us, but what is the intrinsic thing that amazes us? Is it somehow created? Since humans have had the power of reflection, we are trying to understand what sacredness is and how it works on us has been part and parcel of religious practice.
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When people use the word "sacred Space," they usually mean a place of worship of some kind. There is something about the physical placement of a "sacred space" that elevates it above the ordinary. Sometimes a site gets its name from historical events that occurred there. Sacred places have such profound religious significance that pilgrims go from all over the world to spend a few moments soaking in the sacred place.
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1.6.2 Elements of sacred space
Sacredness is the first pioneer on the road to appropriate inner self realisation. For this reason, it creates space for self-realization, educates his external surroundings, and constructs a suitable location for the gathering of others with similar religion, as a defence against the threat of tempest, rain, and ferocious animals. Working through the many structures and design methods in the endeavour to create a space where man may feel holy, certain common design techniques that help to produce the soul stirring experience can be identified. Some of these attributes are as follows.
Sacred Space Elements (Source - pinterest.com)
Space and Volume Space, whether individual or general, has a distinct character of experience. Besides being extremely powerful, it is also quite sensitive. The sense of surround identifies the room as distinct from the surrounding outdoor environment.
Space and Volume quality (Source - archinatureindetail.wordpress.com)
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The individual who enters the area appears as if they are entering a room. Natural or man-made borders (or a combination of the two) define the area within the larger environment. These limits create a subtle sense of protection, allowing visitors to feel comfortable and enjoy their time in the area. Each act movement creates an experience by producing a continuous flow of spaces. Each architectural component becomes significant and provides for this linkage. The point of interaction between volume and space is architectural form. L.S.RAHEJA COLLEGE OF ARCHITECTURE
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Scale and Proportion
The size of one object in comparison to the size of another thing is referred to as scale. A typical architectural problem is determining the size of a sacred place. Some fit into the fabric of the surrounding community and scenery, while others stand out as landmarks, clearly identifiable for their unique function. In general, sacred spaces are built on a massive scale to generate an aura of awe, mystery, and majesty. The grandeur of the internal rooms, the size and weight of the doors, and the exposed structural columns and beams all contribute to emphasise the sacred space’s unique nature. The appropriate or harmonious relationship of one element to another or to the total is referred to as proportion. While the designer typically has a variety of options when it comes to selecting the proportions of objects, some are dictated by nature and man himself. Human body proportions are utilised as a set of measures that may regulate lengths, surfaces, and volumes, not only as numbers with intrinsic harmony. It allows for an infinite number of combinations, ensuring unity with variety, the wonder of numbers.
scale of human to the structure (Source - www.archdaily.com)
Proportional architecture and size connect spiritual architecture to the mathematical framework of the universe. The structure should be able to relate not just to the human size but also to the mind.
Proportion of structure to context (Source - www.archdaily.com)
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Proportion of structure to context (Source - www.archdaily.com)
Light and colour Light is regarded as the most essential component in the defining of space or the expression of form in an architectural space; it not only defines but also gives meaning to the space. This research looks at how light may be used to create a place of worship: how to create a quiet, contained, isolated area, a room full of activity, and a space full of life.
Quality of Light in the Structure (Source - www.archdaily.com)
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Color is the feature that most clearly separates a form from its surroundings. The emotional portion of our brain responds to vivid colours, such as red. Our muscles tighten up first, and then we lean toward the colour. Our heart rate and breathing rate increase, and our blood pressure begins to rise. When we view bright colours like blue, we get the opposite reaction. Our muscles relax, our heart and respiratory rates slow, and our blood pressure falls. Color’s texture is a significant asset. It is the visual and tactile quality imparted to a surface through shape and arrangement, as well as the proportions of the pieces. Texture also influences whether a form’s surfaces reflect or absorb incident light. It adds expressiveness to the surface and so contributes to the overall impression.
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Form and Geometry The fundamental parts, structures, and orders that comprise a sacred space work All of these elements are perceptible and experienceable. Some may be obvious, while others may be more mystifying to our mind and senses. Some may predominate, while others serve a supporting role in spatial awareness. Some may communicate pictures and meaning, while others function as qualifiers or modifiers of these signals. These parts and systems must be interconnected in order to produce an integrated whole with a unifying or cohesive space. Sacred space is generated when the arrangement of pieces reveals their ties to one another and to the design as a whole. Because this analysis is dependent on geometry in many ways. Geometry is represented in form and shape in many cultures. Geometry is seen in the design as a space sequence and in the details. It is used to visualise the entire architecture of space, and ideologies are connected to them.
Form of Sacred Structure (Source - www.archdaily.com)
Form refers to both the interior and exterior layout of space, as well as the concept that brings unity to the whole. However, the majority of spaces are focused on the exterior configuration of form. While form frequently involves a feeling of volume, shape refers to the fundamental characteristics of form that determine its appearance. In addition to shape and form, visual characteristics such as size, colour, and texture exist. Forms contain relational qualities that control the pattern and composition of elements, as well as location, orientation, visual inertia, and so on.
Sacred Structure (Source - trendhunter.com)
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Source - designcurial.com
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1.6.3 Geometry as important part of sacred space Geometry is the science of the characteristics and relationships of magnitudes such as points, lines, surfaces, or objects in space, as well as the way the components of a certain item fit together. Geometry is well recognised because it is based on two Greek words: "geo," which means "earth," and "metry," which means "to measure." Geometry literally means "measuring of the earth" or "earthly measures." According to Plato, geometry can also apply to the study of stereometry or "spatial measures."
Importance of Geometry in a Sacred Space (Source - trendhunter.com)
Geometry has been used in a variety of structures and architectural styles for centuries. The ancient Greeks, particularly Pythagoras and Plato, are credited with the first verifiable record of geometric knowledge and its link to astronomy, humanity, and music. Prior to the Greeks, however, numerous ancient civilizations left unmistakable geometric imprints by employing sacred geometry in their buildings. The prehistoric engraved stones resembling the Platonic Solids discovered in Scotland may be traced to over a thousand years before the Greeks. In all ancient civilization, geometric ratios and proportions existed and were used in the design of ancient sacred and ceremonial places. They were usually designed with dimensions that include mathematical quantities, constants, and ratios such as the "golden/sacred mean," as well as the usage of proportional roots, proportional rectangles, and Pythagorean triangles.
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The goal of design geometry is not to quantify aesthetics through geometry, but rather to disclose visual linkages that have foundations in basic living aspects such as proportion and development patterns, as well as arithmetic. Its goal is to provide insight into the design process as well as aesthetic coherence to the design through visual structure. This understanding allows the designer to find worth and value in themselves and their own work. Geometry has a vital purpose in expressing the visual relationship of an object based on its proportion as well as the object’s growth pattern. Geometry was adopted in mythology, religion, many spiritual traditions, alchemy, mysticism, and so on. Geometric form symbolism governs the structure of space and the shape of objects. Understanding the significance of geometric patterns gets us closer to knowing God. Each geometric figure can be interpreted allegorically as a type of map containing a portion of the enormous knowledge about the structure of the world, man, and the Universe. Knowing the Divine can be aided by understanding the language of geometric forms.
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“Sacred Geometry is a pattern behind everything – a blueprint of the creation.” - Seedartha
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WHAT IS SACRED GEOMETRY? The language of the cosmos is sacred geometry. It is the creative recipe that gives existence life. Its dynamic architecture is shown to us through shape, pattern, and number. It offers the vibrational blueprint for matter’s creation, and we can see these archetypal designs at action in everything from the subatomic to the cosmic scale. It may be seen in the division of our cells, the unfolding of a rosebud, and the planets’ orbits. Relationships are essential to geometry. It defines how every shape – living or inanimate – compares to itself or another. It is not a new concept; it is present in all things.
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“Philosophy is written in that great book which ever lies before our eyes – I mean the universe – but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.” -Galileo Galilei (1564–1642), astronomer
Sacred geometric forms create blueprints for design (Source - Sacred Geometry by Jemma Foster)
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2.1.1 UNDERSTANDING OF SACRED GEOMETRY
Geometry of Universe (Source - shutterstock.com)
Our physical world exists in Space and Time. Modern esoteric knowledge has shown the practical potential of working with Space’s forms. Sacred geometry is the theory of Space’s forms and the rules of Being’s evolution in line with these shapes. Geometry is an intriguing field of mathematics that studies the relationship between shapes and spaces. It enabled the creation of numerous practical concepts as well as artistic and spiritual expressions, making it the most stunning field of mathematics. The physical world we perceive is the product of a complicated network of interactions, correspondences, and flirtations that start on invisible levels beyond our awareness. There is a conscious, organising principle at the start of our consciousness that transcends explanation by science and reasoning alone. It is not a brain generated consciousness, but one that is primitive and vast, a generative life force at work weaving the fabric of the world together.
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Those who believe in sacred geometry believe that everything in the cosmos was created by god using geometrical rules and so God is regarded as the world’s geometer or architect. From the tiniest particles, such as the atom, to the bigger universe, each creation of nature follows a precise geometric design, which can be seen in their shapes, patterns, ratios, and frequencies. The symbolic and sacred values of specific geometric forms and proportions are the foundation of sacred geometry. These forms are a significant tool for spiritual development. Understanding sacred geometry’s fundamental truths leads to awareness growth and heart opening, which is the next stage in personal progress.
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It is the study of the hidden meanings underlying geometric shapes in order to comprehend the cosmos. It is thought that inside these forms resides the secret of every element and facet of this world, and that understanding these secrets can help us humans grasp the Great Mysteries and the Great Design that serve as the foundation of this universe. For thousands of years, sacred geometry has played an important part in the art, architecture, and philosophy of many civilizations. Geometric ratios and geometric forms were frequently used in ancient Egyptian, Indian, Greek, and Roman architecture. Symbolic geometry was extensively used in mediaeval European churches. Indian and Himalayan spiritual groups frequently built temples and fortresses based on mandala and yantra architectural designs. Sacred geometry is a science that integrates the tangible components of creation with the spiritual essence. It is the meeting of the visible and the unseen, the manifested and the unmanifest, the finite and the infinite. It allows us to examine God’s manifestations and diversity in the cosmic order of things. This concept is particularly prevalent in Islam and Hinduism. Mosques hold numerous keys to the structure of the Cosmos, as well as emblems of the world as God’s creation. The geometric forms of several ceremonial and occult buildings are comparable. It refers to the mathematical formulae that serve as the foundation for everything. It is the meeting point of thought and matter, spiritual and physical, manifest and unmanifest, bound and limitless. Sacred geometry may be found in the foundations of everything on our planet that supports life. As a result, whether we are conscious of it or not, we are always interacting with sacred geometry. Sacred Geometry and Chakras (Source - pixels.com)
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2.1.2. DIFFERENTIATING GEOMETRY AND SACRED GEOMETRY
Sacred geometry is associated with geometry in the same sense that chanting is associated with singing or sacred dancing of a whirling dervish is related to dance. Geometry serves a sacred significance. Sacred Geometry is pure mathematics combined with the understanding that everything is energy and that energy is spiritual. Patterns, proportion, and ratio are expressions of the Universal Divine that transcend religion, dogma, and society, and share many similarities with quantum physics.
Scientific Geometry (Source - sciencedirect.com)
Sacred Geometry is the language of Spirit and, at its most basic, the language of creation. It is a numerical language used in art, music, and architecture. Nature’s ratios, such as the Fibonacci series and the Golden Ratio, control both the visible and invisible worlds. Every sacred shape is a creative word, a kind of vibrational energy and pattern that expresses Source’s creativity.
“The whole inhabited earth is a sacred space in which God lives, breathes, and acts.” — Carter Heyward
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2.1.3. ORIGIN AND HISTORY
Geometry is described as "the branch of mathematics concerned with the study of space and the connections among points, lines, curves, and surfaces." This concept corresponds well with the rationalism-based academic study of geometry. Geometry has an emotional aspect, and particular geometrical shapes and proportions have sacred meaning. This concept might be considered the foundation of sacred geometry. It is a concept and technique that may be found in many civilizations across the world. Geometry is thought to have originated as a technical study as a result of everyday problems. The first geometry practitioners devised a set of principles for calculating lengths, areas, and volumes. Many of these, on the other hand, were rough guesses based on trial and error. Geometry was invented by the ancient Egyptians, according to Herodotus. Written evidence from Egypt backs up this claim. Nonetheless, the ancient Mesopotamians, as well as the ancient Chinese and Indians, are known to have explored geometry.
Origin of Geometry (Source - emaze.com)
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Geometry and Nature (Source - medium.com)
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Around the 6th century Bc, the Greeks got fascinated in geometry, transforming it from a practical to an abstract study depending on analogies. This area of mathematics also gets its name from the Greeks, as it is a mixture of two Greek words, geo (earth) and metron (number) (measure). Although numerous Greek and Roman intellectuals contributed to the discipline, none had a larger influence than Euclid, who is often regarded as the founder of geometry. Euclid lived in Alexandria during the 4th and 3rd century BC and is most known for his Elements, one of the most significant works in mathematical history. Elements is a wonderful example of a reasonable and scholarly approach to geometry studies. Other classical philosophers contributed to the study of geometry, some of whom had a diverse approach to the topic. Because these philosophers recognised symbolic and sacred significance in geometry, their branch of study is known as sacred geometry. The Pythagoreans were a school of these philosophers, whose school of thought was founded by Pythagoras of Samos.
Geometry of Nature (Source - newearthknowledge.com)
Plato, the ancient Athenian philosopher, rediscovered these unique shapes for the first time in 360 B.C. and he regarded them to be highly significant shapes; hence, these solids are known as platonic solids. They include every conceivable chemical link as well as the geometric rules of existence and the cosmos.
Geometry in Architecture, Math and Art (Source - bleckarchitects.com)
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Sacred geometry began to evolve in many cultures, and man connected numerous theories to geometrical forms. These shapes and symbols are found throughout Hinduism and have several meanings. In accordance with the cardinal Points, the ‘square’ depicts the ‘earth.’ It is also considered to be a deity’s dwelling. It is a mystical, absolute, and fundamental geometric element. Because of its religious foundation, it does not allow for any modifications during the transition process. The triangle represents the Indian Trinity and is the primary ruling element. People constructed fundamental geometric forms based on natural forms. The ‘circle’ is seen as a symbol of eternity in Islam, a shape with no beginning or end. The Square is seen as the most intangible form of creation and a symbol of the ‘earth.’ The dome is said to be a representation of heaven. These diverse basic geometric shapes were first used in sacred structures.
The evolution of Medieval European structures was frequently based on geometries meant to help the observer comprehend the world through mathematics and get a greater knowledge of the divine via this understanding. At the beginning of the Renaissance in Europe, attitudes changed toward simple and regular geometries. The circle, in particular, became a prominent and symbolic shape for constructing foundations, representing the purity of nature and the primacy of man’s role in the cosmos. The circle and other basic and symmetrical geometric shapes were a mainstay of Renaissance holy constructions that defined the ideal space in terms of sacred geometry.
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THE FORMS AND PATTERNS In nature, Human kind explores the structures and patterns from the most miniature particles, to the manner of life observable by human eyes, to the greater cosmos. These patterns certainly obey geometrical prototypes, which disclose the nature of forms and their vibrations. They represent the primary metaphysical principle of the inextricable relationship of the part to the whole. The architecture of all forms permeates the principle of oneness, interconnectedness and union and reminds us of our relationship to the whole, it is a layout for the mind to the sacred foundation of all things created.
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2.2.1. CIRCLE
The circle was one of the earliest shapes drawn by human kind. It was simple to draw, visible in the surroundings of everyday life, materializing in the form of animals and plants and geological natural bodies. The geometry of the circle is as endless as the circle itself, and is considered to be a sacred symbol by almost every known culture on Earth. It is said to be humanity’s earliest symbol, and it has been utilised by all cultures throughout history. The Circle represents eternity since it has neither beginning or finish. It is possible to draw it using just one line. The celestial bodies of the Sun, Moon, Planets, and Earth all have circular forms. In a wedding ring, this ring shape is considered as a symbol of devotion.
Geometry of solar eclipse (Source - nationalgeographic.com)
It’s not hard to figure out why, circle began to be thought of as a sacred body. We saw two circular bodies moving through the sky around us on a daily basis, the sun and the moon. The sun was worshipped by many ancient people for warmth and light. On the other hand, during the night the moon was often seen as a companion having complimentary energies and powers. The circle represents the inclusivity of the universe and the infinite nature of the energy through its sacred and divine nature.
Geometry of circle (source - 123rf.com)
It is the most common and universal sign, found in all cultures. It has no beginning and no end, and no divisions, making it the perfect representation of completeness, eternity, and the soul. It also represents the sun in its limitless or boundless aspect. The circle is also the symbol of boundary and enclosure, of completion, and returning cycles.
Geometry of Moon (Source - joy-pup.com)
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Sacredness of circle (Source - en.wikipedia.org)
Since ancient times, structures were mostly circular, whether temporary or permanent. From the circular hut of Neolithic Britain, through the megalithic stone houses, to circular temples and churches, the roundness of the visible horizon has been emulated by the circular form, establishing the impact for each building by itself.
Arrangment of Stone Henge (Source - cen.acs.org)
“God is a circle whose centre is everywhere and whose circumference is nowhere.” -Hermes Trismegistus
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2.2.2. SPHERE
A sphere is a spherical, three-dimensional object. A sphere, unlike other threedimensional forms, lacks vertices and edges. All of the locations on the sphere’s surface are equidistant from its centre. In other words, the distance from the sphere’s centre to any point on its surface is equal. There are numerous real-world things that are spherical in shape that we see around us. A sphere has a volume and a surface area since it is a three-dimensional form. Our planet Earth is not a perfect spherical, yet it is referred to as a spheroid. Geometry of Dandelion Flower (Source - pixabay.com)
Geometry of Sphere (Source - geometrycode.com)
One beautiful mathematical formation found in nature is the perfect sphere. A perfect sphere is described as being perfectly symmetrical around its centre, with all points on the surface being the same distance from the centre point. While the Earth is frequently referred to as spherical, it really fails this categorization because it is somewhat flattened at the poles. Nonetheless, a perfect spherical does exist in nature and may be observed in bubbles, water drops, planets, and atoms. In addition, the sun is said to be the most perfect sphere ever observed in nature.
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Why are these perfect spheres so crucial to nature and our persisted existence? The world would not work as we know it if spheres were not balanced with one another. Balance is essential for life on our planet, and nature has always found a way to balance perfect spheres throughout time. Nature is predictable and mathematical because of the balance of spheres. Many objects in nature, such as bubbles, planets, and atoms, are shaped into spheres by gravity and force. These spheres would not exist if they were not balanced. Nature would not arise as a consequence.
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Geometry of Planet (Source - scientias.nl)
The earth, sun, moon, and stars are all inextricably linked to spheres. They are a wonderful instrument for open0.ing the third eye chakra, which increases intuition and clairvoyance. In crystal therapy, it can be transmitted through the aura or held over the chakras. It instils a calm and grounded atmosphere in the home. The sphere is also an excellent centre in grids for earth healing, harmony, protection, and psychic growth. Grids always necessitate a bigger central stone that serves as the primary source of energy to focus on. A spherical in the centre with the potential to radiate outward in all directions is the best shape choice. Pyramids and obelisks can also be used as grid centre stones.
“God is a sphere whose center is everywhere and whose perimeter is nowhere.” ~Voltaire Geometry of Bubble (Source - needpix.com)
Geometry of water droplets
The roundness of the sphere symbolises oneness, wholeness, completion, karma, and reverence for cyclical forces. The sphere’s smooth surface allows for clear communication and aids in keeping the energy flow going. Sphere aid in the empowerment of the mind by directing supportive healing energies through the conscious body. Moving energy through time, spheres can let you perceive things from a new angle. Sphere may be useful in cleaning and repairing auric field leakage. In times of stress, spheres make wonderful "hand comforters."
(Source - pixabay.com)
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2.2.3. TRIANGLE
The Sanskrit sign for the Third Eye Chakra contains it. A Triangle, when pointed up, represents a flame and fire, or a torchlight that lights the darkness. It becomes a masculine emblem that connects with the divine and raises energy skyward. A Triangle becomes a cup that contains water or a vessel of spirit when it is reversed. It then transforms into a feminine symbol that balances energy or receives spiritual information.
Geometry of Triangle (Source - pixabay.com)
Triangle is one of the most intriguing forms. The triangle is a symbol of a trinity since it is composed of three lines and has three points. This might represent the Holy Trinity, the Triple Goddess, or Mind, Body, and Spirit. It is produced when two distinct points combine to form a third point, which is balanced. The triune nature of the Universe - earth, heaven, and human – is represented by the triangle. One of the most powerful and universal symbols is the triangle. One of the original and most important planar figures in Sacred Geometry. Triangle arose from the chaos that preceded creation as the first cosmic form. Triangle inside a circle represents triune, the universe of forms encircled by eternity. Swastika inside a triangle represents cosmic harmony. Three ray triangles symbolise an old type of World Triple Light.
Sacredness of triangle (Source - pixabay.com)
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“In the ladder of creation, Triangle belongs to the World of the Gods.” Geometry of triangle in architecture (Source - pixabay.com)
History and Culture This shape was held in high regard in many ancient civilisations. In antiquity, the triangle was connected with the formation of the Milky Way and three stars - Deneb, Vega, and Altair - that formed a triangular shape in the sky. The equilateral triangle represents the light of life in the Chaldean faith. The same shape symbolises light in Greek, a symbol of health and knowledge. The triangle was a symbol of lovely and rich land in ancient Egypt. In Hinduism, the point-down triangle represents feminine vitality. The Shakti principle is associated with water and the power of the subterranean kingdom. The masculine energy principle was represented by the point upwards triangle.
It represents fire and divine power. Combining two triangles results in the formation of a six-pointed star, which represents the union of the male and female principles, as well as the glorious victory of spirit over matter. In ancient Europe, a triangle with a tip upwards indicated a tongue of flame and a masculine fire. The water that flows down from the mountain peaks to the land was symbolised by the point down triangle.
Energy of Triangle (Source - pixabay.com)
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2.2.4. FRACTALS AND RECURSIVE GEOMETRY
Fractal forms appear in different aspects of our daily life surroundings. These forms are nothing but the mathematical shapes with infinitely complex structure. They are never ending repetitive patterns, which regardless of how zoomed out or zoomed in, it shows the similar image. The fractal comes from the Latin word which is fractus which is defined as ‘broken’ and it has been formed by the italian mathematician Benoit Mendelbrot. Once we get aware of the basic theory of fractals, it is astonishing to see the existence of fractals in nature around us in unique and different ways. It is most commonly found from the branches of trees, animals circulatory system,snowflake to plants and leaves, geographic terrain and river system,and crystals. Fractals and sacred geometry are patterns of energy which show reality at mystic level. The understanding of use of these geometries to create matter and life at the elementary level, helps to be aware about energies of creation which lay the foundation for the universe. Fractals and sacred geometry contain the simple and complex mathematical formulas of energy of creation which witnessed the reality and life. These geometries were never created but rediscovered while playing with mathematical formulas.
Fractal Forms development (Source - medium.com)
“Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” SHRAVAN PADATE/FIFTH YR. B.ARCH
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The following characteristics are frequently seen in fractals: 1. At an extremely micro scale, it possesses a fine structure. 2. It’s just too irregular to be defined in traditional Euclidean geometric terms. 3. It resembles itself (at least approximately or stochastically). 4. It has a Hausdorff dimension that is higher than its topological dimension (however space-filling curves like the Hilbert curve do not meet this condition). 5. It has a concise and recursive definition. Fractals and sacred geometry are outlines of energy of creation. The energies used by the geometries in specific patterns which allow them to shape matter into specific form. On every scale of tangible as well as intangible reality, everything is affected by sacred geometries. The structures of our DNA, the shapes of clouds, the patterns of snowflakes, the cornea of our eyes, the shapes of crystals, the star we spin around, the galaxy in which we spiral, and all forms of life originate from geometric patterns and codes.
Fractal Energies (Source - shutterstock.com)
Energy efficiency is important in nature, and high-performing buildings are built with basic materials and knowledge as the key to success. Nature has devised an astonishing ratio between the quantity of information given into the system and the complexity of the output in order to reduce the amount of energy and material spent on this information. Self-similar structures require only one rule that applies at all sizes, and fractal structures are generated by being information efficient.
Infinite fractal perimeter (Source - quora.com)
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Fractal patterns may be found in the network-like branching patterns of ferns, trees, roots, leaves, and fungal mycelium in the soil. They may also be found in the patterns of streams, rivers, coasts, mountains, waves, waterfalls, and water droplets in the natural world.
1. Trees In nature, trees are great representations of fractals. Fractals may be found throughout the forest ecosystem, from seeds and pinecones to branches and leaves, as well as the self-similar reproduction of trees, ferns, and plants.
Fractals in tree branches (Source - theconsciousvibe.com)
2. Rivers In nature, trees are great representations of fractals. Fractals may be found throughout the forest ecosystem, from seeds and pinecones to branches and leaves, as well as the self-similar reproduction of trees, ferns, and plants.
Fractal in rivers (Source - theconsciousvibe.com)
3. Mountains Over millions of years, the forces of nature sculpted several mountain ranges. The movement of glaciers and water in Western Canada has fundamentally sculpted these mountains.
Fractal in mountains (Source - theconsciousvibe.com)
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4. Plants Leaves and root systems have a fractal structure in the manner they develop from the sun’s light. With the Romanesco Broccoli from Italy, you get a beautiful example of fractal structure.
Fractal in Plants (Source - theconsciousvibe.com)
5. DNA In nature, trees are great representations of fractals. Fractals may be found throughout the forest ecosystem, from seeds and pinecones to branches and leaves, as well as the self-similar reproduction of trees, ferns, and plants.
Fractal in Human DNA (Source - theconsciousvibe.com)
6. Galaxies As above, so below. At the lowest level possible, atom characteristics display fractality, while at the macroscopic level, the Milky Way Galaxy, solar systems, and potentially the entire fabric of the Universe exhibit a similar fractal pattern.
Fractal in Universe (Source - theconsciousvibe.com)
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2.2.5. VESICA PISCIS
The Vesica Piscis is a geometric composition made up of two circles of equal radius crossing in such a manner that the centre of one circle is on the perimeter of the other. In the intersection of the circles, this geometric shape may be extended to produce two consecutive equilateral triangles with opposing orientation.
Vesica piscis
Vesica piscis and spirituality
(Source - boanerges.edu.pl)
(Source - tattoodaze.com)
The circle has no vertex, no beginning, and no end, making it a symbol of the boundless or ideal in almost every ancient culture. The sun, the source of life, as well as numerous deities, are all represented by the circle. As a result, it’s only natural that two circles linked at an intersection appear in a range of cultural contexts. The most intuitive option of intersection for two circumferences is to link the centres with the perimeters, even if you have no formal understanding of geometry. As a result, the Vesica Piscis structure may be found in artefacts from many different civilizations.
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The Mandorla, which means almond in Latin, is another name for this form. The term piscis, like the astrological sign Pisces, is derived from the Latin word for fish and serves as the basis for the Christian fish emblem. This form can also be found in mediaeval paintings of Christian holy figures who are connected with rebirth and change. It may be found in the petals of lotus flowers, plant and tree leaves, lemons, and fruit seeds in nature.
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Origin and history ‘Vesica Piscis,’ which literally means ‘fish bladder,’ is usually related to Vesica Pisces, which refers to a single fish bladder. The word’s origin is generally linked to religious or mystical origins. Even if no one knows for sure where the name Vesica came from, it appears to have been a popular term for a conduit or sack formed by animal bladders. The word was also used as a vulgar slang name for the vagina, referring to both form and an earthy or animal odour. It, as a depiction of the vagina, would have two socio-cultural meanings in this context: as a male object of desire and as a feminine emblem of motherhood and creation. The Vesica Piscis has a long history of being associated with female genitals. Palaeolithic depictions of female vulvas may be found in numerous caves containing prehistoric art, particularly in northern Spain and southern France. The fish was Jesus of Nazareth’s emblem in Christianity, portrayed by a Vesica Piscis-like graphic structure. The Vesica Piscis sign with a tiny addition resembling a fishtail was used to symbolise Christ and his teachings, and the Vesica Piscis symbol with a small addition resembling a fishtail was used to represent Christ and his teachings. This feature might have been just decorative or it could have been intended to designate a direction, as it was when Christians needed to worship privately. Other Christians might see the sign and know where they could worship.
Evolution of vesics piscis (Source - flickr.com)
Two converging circles, representing the Spiritual and Physical Worlds, make up the Vesica Piscis. It forms a shape that depicts the feminine gateway to new life and birth.
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The seed of life and flower patterns develop when the ancient vesica piscis sign is repeated several times in a specific geometric pattern. There are a plethora of mystical connotations connected with each of these symbols. Both depict the creation cycles and illustrate how everything comes from the one. Six distinct vesica piscis are produced between each surrounding circle in the Seed of Life, as well as an inner rosette of comparable but smaller lenses. The central circle crosses each of the surrounding circles, resulting in an additional six vesica piscis.
Vesica piscis in Nature (Source - quotesgram.com)
The vesica piscis shape may be found in many places in nature, including buds, leaves, fruits, and seeds, as well as the fundamental body shape of many animals including birds and fish. Seed pods and the chrysalis are examples of vesical structures that are both protective and transitory. The pupating caterpillar is housed in the chrysalis above, which is supported by a braided thread and has a spherical ceiling created by the monarch butterfly. In nature, the vesica piscis is part of a network of linked living forms, rather than standing alone.
Vesica piscis and spirituaity (Source - quotesgram.com)
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2.2.6. SPIRALS
Spiral is one of the oldest symbols known. It may be seen carved and painted all over the world on cave walls and rocks. This shape was admired by the Celts and the Maori. The Spiral depicts a route of concentrated movement and heightened energy. It can be found in shells, ferns, Galaxies, and even our DNA strands in the natural world.
Geometry of Spiral
Spiral in Architecture
(Source - iconspng.com)
(Source - agefotostock.com)
Heaven and earth are interlinked by the phrase "as above, so below." The spiral ascends to connect the physical self to the Higher Self, as well as all layers of our existence (interdimensionally) and the Earth’s core. Galaxies are arranged in energy spirals. Energy moves in spirals. The spiral also represents the kundalini, which represents increasing one’s awareness on the path of soul growth. As the chakras rotate in a circle, the spiral represents the flow of energy through them. Each cell’s DNA has a spiral structure in the form of a double helix.
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Change is brought about by life cycles and natural world cycles. The old must pass away in order for the new to emerge. Each of us grows from a toddler to an adult to an elderly person. As a result, the spiral is a symbol of change, advancement, and development rather than stagnation. It accepts these things as good and healthy, and it aids in the acceptance of change, despite the fact that we are frequently better at ease withdrawing into tradition and old, conventional methods.
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Watery symbols are sometimes associated with spirals. Water is a changeable substance that is always changing and has no permanency. It also ripples in a circular motion. Finally, water, like earth, is a feminine element.
Spiral in Plants (Source - treehugger.com)
In nature, spirals and circles are far more prevalent than straight-edged forms such as triangles and squares. As a result, people nowadays tend to connect spirals with nature rather than the built, mechanical, and urban environment. Spirals are natural, unadulterated, and unconstrained by man. Furthermore, ancient people were well aware of nature’s cyclical forces: monthly lunar patterns, yearly solar and seasonal patterns, all of which influence yearly patterns in plant and animal husbandry. Because at least some of the ancient spirals have been claimed to symbolise the sun, it is frequently referred to as a solar sign. Solar symbols, on the other hand, are primarily male-oriented, hence their usage in modern beliefs is limited.
Spiral in ancient art (Source - zhirayravetisyan.com)
A spiral can be used to symbolise cosmic time cycles, the Milky Way Galaxy, or even the whole Universe. It can represent the Kundalini’s coiled serpent-like energy at the base of the spine, or the Root Chakra. Since ancient times, snakes have been connected with intelligence and understanding. Some people believe that the Chakras themselves resemble a spiral of light.
Spiral in solar system (Source - steemit.com)
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2.2.7. MERKABA
The Merkaba is a symbol of great power. It’s made out of two star tetrahedrons, one looking up to the sky and directing energy down from the Universe to the earth plain, and the other pointing downwards and pulling energy up from the ground below. The top, or upward pointing tetrahedron, spins clockwise, while the bottom, or downward pointing tetrahedron, rotates counterclockwise.
Geometry of Merkaba (Source - shutterstock.com)
The term Merkaba may be broken down as follows: MER: revolving fields of light, KA: spirit, and BA: soul (this is from an Egyptian translation from the 18th dynasty, and it means ‘chariot’ in Hebrew). As a conclusion, Mer-Ka-Ba corresponds to a spirit or energy body encircled by counter-rotating fields of light or spirals of energy (similar to a strand of DNA) that carry spirit or awareness from one dimension to another.
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Merkabah mysticism is an early Judaism school that flourished between 100 BCE to 1000 CE. The lessons were based on visions from Ezekiel’s book and hekhalot literature. These tales depict ascensions into the skies and to God’s Throne. With meditation practise, anybody may access their own unique Merkaba or vehicle of light. It is claimed that having access to one’s Merkaba may give strong protection as well as move one’s awareness to higher realms. When we link our bodies’ energy to Source, the Merkavah symbol can remind us of the potential power we have.
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The Merkaba emblem has long been connected with Hebrew tradition, followed by Christianity. The term comes from Hebrew and means "light, soul, and body." The Merkaba Sacred Geometry represents the coming together of opposites. It brings together light and dark, masculine and feminine energy, the physical and spiritual worlds. It signifies fire components and is connected with kindling our inner flame or light of life since it comprises tetrahedron pyramid forms. The Divine and higher knowledge are connected with the tetrahedrons in its structure, offering us more awareness and assisting us in connecting with source. The Merkaba sacred geometry tetrahedron’s upper point connects us to God or spirit, while the downward point ties us to Earth and gives us a sense of groundedness. Concept of Merkaba (Source - thebluebudha.com)
Energies of Merkaba (Source - behealthywithana.com)
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The Light Body vehicle, or MerkaBa, is the key to learning how to travel between dimensions or planes. It is the divine light vehicle that Ascended Masters are said to utilise to interact with and reach individuals who are tuned into the higher realms. You are in a state of total safety when this form is activated around your body, with the surrounding energy being created from pure Divine Love. With practise and the energy and shape imagery of a Merkaba, it is thought that you may generate an energy field around you that can take your awareness directly to higher worlds. Ascended masters are said to have used this symbol to connect to higher worlds since it blends conflicting forces in perfect harmony. The Merkaba is regarded as an interdimensional vehicle in current esoteric teachings. It’s also called a star tetrahedron, and it looks like a three-dimensional Star of David.
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2.2.8. METATRON’S CUBE
Geometry of Metatron’s cube (Source - shutterstock.com)
Metatron’s Cube is a symbol that represents the journey of energy across the cosmos, as well as the equilibrium that exists within it. It contains all of the Platonic Solids, as well as thirteen circles to symbolise the thirteen archangels (with Metatron’s circle in the middle). All of the circles are also joined by straight lines, representing the feminine and masculine as inextricably linked, demonstrating that everything in the cosmos is related to everything else. If you pull on one thread, it can ricochet across the entire system, similar to the Butterfly Effect.
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The Cube also represents the movement of energy throughout the cosmos. While the source of the energy may be the tree of life that Metatron protects (or the throne of God, depending on your interpretation), it flows via him and the other archangels to the farthest point of all creation. Metatron’s cube includes every shape that God made in the cosmos, and those shapes are the building blocks of all physical substances. They are known as Platonic solids because Plato associated them with the spirit realm of heaven and the physical elements on Earth. Those three-dimensional forms may be seen in anything from crystals to human DNA.
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Metatron’s cube in nature (Source - wdrfree.com)
The term Metatron originally emerged in Jewish Kabbalistic and Talmud literature and is said to be the name of an angel or a guardian. According to Jewish tales and traditions, this angel formed the cube with his soul. Metatron’s cube symbolizes all geometric shapes found in all things and is linked with the concept that the deity is the universe’s geometer. Metatron’s cube comprises all of nature’s most frequent forms, such as circles and lines. Technically, it consists of 13 circles connected by straight lines drawn from the centre of each circle. A centre circle is encircled by six circles that form a flower-like pattern, and another set of six circles extends from it.
Metatron’s cube and Platonic Solids (Source - sagegoddess.com)
The sequence of linked lines form diverse forms known as Platonic Solids, which are considered to constitute the foundation for all design in the world. Pyramids, cubes, octahedrons, dodecahedrons, and icosahedrons are examples of these forms. The ancient Greeks associated these mathematical forms with the fi ve elements since they appeared regularly and randomly in nature.
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2.2.9. FLOWER OF LIFE
Flower of Life (Source - shutterstock.com)
The Flower of Life symbol is a two-dimensional graphic made up of 19 equivalent overlapping circles. Not only is the composition fascinating; it also has significant symbolic significance for our existence, life on Earth, and the genesis of the Universe. The Flower of Life is made up of more basic forms or structures. The design begins with a vesica piscis, a geometrical form made up of two overlapping circles of the same size. Additional circles are formed by combining the two spheres. The Seed of Life is a similar pattern, but with only seven linked circles. It serves as a foundation for the Flower of Life design. The Flower of Life may be found in various civilizations all around the world. Sacred Geometry is an ancient language that spans all civilizations and species on our planet and beyond.
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The first known example of the Flower Of Life emblem may be found in Ancient Egypt. Wall reliefs at the Temple of Osiris exhibit engravings from at least 6,000 years ago, etched into the Osirion building in Abydos, Egypt. This was unearthed in the twentieth century while archaeologists were working on the Seti Temple. The "Osirion" was completely submerged beneath the sands of time.
Elements of Flower of life (Source - imgur.com)
Leonardo da Vinci is claimed to have associated the Flower of Life with three other symbols known as the "Egg of Life," "Fruit of Life," and "Seed of Life." Da Vinci seems to be interested in the mathematical characteristics of the symbol. The lengths between the spheres are supposed to be similar to the intervals between tones and half tones in music, therefore the ‘egg of life’ is said to provide the foundation for music. It also has the same cellular structure as the third embryonic division - the initial cell splits into two cells, then four cells, and finally eight cells. Thus, as it develops, this same structure generates the human body and all of the energy systems.
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Significance in Different cultures and religions
Judaism The Tree of Life is a popular symbol in Judaism and is thought to have evolved from the Flower of Life. The Tree of Life is made up of ten spiritual symbols known as the Sephiroth. Each Sephiroth represents a different element of God, and when they are arranged in the Tree of Life, they form the name of God. The 10 Sephiroths are sometimes referred to as the Chakras in Judaism, each of which corresponds to a distinct energy within the human body. In Kabbalah teachings, the Tree of Life represents the ‘concept of shared descent.’ This tree of life is said to be comparable to the tree of life described in the Book of Genesis. Tree of Life in Judaism (Source - dreamstime.com)
Christianity Numerous parallels have been seen between the Flower of Life and Christianity. The Seed of Life is especially significant in Christianity because it represents the seven days of creation with its seven interlocking rings. The Tree of Life is situated within the Flower of Life and is linked with the Tree of Life.
Seed of Life in Christianity (Source - tumblr.com)
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Egypt Archaeologists found the Temple of Osirion in the ancient Egyptian city of Abydos, which was located beneath, but related to, the Temple of Seti I. Osirion contains massive red granite pillars. The temple was most likely constructed between 1294 and 1279 BC. Years later, likely in the first century AD, someone used an ochre stain to draw Flower of Life motifs on the pillars. There are numerous advantages to the bloom of life. It is most well-known for its spiritual field. Vibrations and a calming ambience may be felt by placing the flower of life in a location conducive to meditation and personal contemplation. We may feel peaceful and relaxed, and we can dispel all of the bad energy, tension, and anxieties that collect in our everyday life. The bloom of life emits powerful and steady waves that enable for expression and spread. It disseminates energy, which helps to balance the ecosystem. The flower of life also possesses the qualities of renewal, balance, dynamism, and protection.
Evolution of Flower of Life (Source - crystalinks.com)
Sacredness of Flower of Life (Source - onetribeapparel.com)
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SIGNIFICANCE OF FORMS AND PATTERNS Geometric forms and patterns are seen to be intriguing but not especially helpful by most people, unless they are a mathematician, architect, or engineer. The evidence, on the other hand, is contrary, and it has been recognised for thousands of years and in almost every religious and cultural tradition. Even in our culture, where sacred geometry is neglected or despised, geometrical structures are essential to our knowledge of ourselves and all elements of manifestation—physical, mental, and spiritual. The use of forms and patterns in a lineage-based manner provides us the ability to connect with the divine no matter where we are. It helps us to cross the gap between the physical and spiritual worlds by uniting them. In many respects, using holy geometry may assist us in creating heaven on earth within that specific area. Their significance stems from their enormous creative power. In the abstract symbolism of geometry, these structures depict the points at where the "universes" of the left and right cerebral hemispheres collide. Even on a physical level, the act of converting the linear into the holistic is incredibly creative, with profound spiritual implications. Forms and Patterns are crucial to our knowledge of the universe, and they are an essential component of every mathematical curriculum. The significance of them is sometimes lost in a repeated pattern of two-dimensional forms. In mathematics, forms and patterns are much more than a repeating pattern of objects. We develop an appreciation and knowledge of the world in which we live and how everything is related by studying natural shapes and patterns. And, through connecting with Nature, we develop a stronger connection with our spiritual selves. A kaleidoscope of visual shapes and patterns – both living and nonliving – surrounds us. Our perception of forms and patterns greatly influences our knowledge of people and things, and our understanding of people and things influences how we treat them. When we arouse people’s emotions, we arouse energy that can impact how we are treated and how we feel as a result. When we comprehend this cycle, we empower ourselves to control the energy circulating about us in our surroundings more wisely, which, if not understood, can cause conflict. Once the energies are recognised, they may be harnessed to accomplish the desired outcome.
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“I think the universe is pure geometry – basically, a beautiful shape twisting around and dancing over space-time.” — Antony Garrett
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EXISTENCE OF GEOMETRY IN NATURE Sacred geometry is the focal point between physics and spiritual world. It is the monarchy where the unbounded live within bounded forms, and the havoc of creation is brought to order. The true beauty of sacred geometry is that it satisfies all the elements around us including the human body. Math is all around us, it’s a well-known fact. It influences how we live our lives and can be found in almost everything we engage with, from video games and music to nature and cuisine. Geometry is one such part of math that may be found in nearly every area of our environment. Geometric forms, symmetry, and the golden rectangle have all served to shape the world around us, whether it’s a man-made structure or an organic lifeform. When we take a close look, the sacred geometry appears everywhere from tiny plants to big animals. The plants grow oriented under same degree creating spiral which defines the perfect work of Fibonacci sequence in nature, Perfect geometric formation of crystal inside the rock showing how great creator of universe is, DNA is a blueprint of life, which form by the perfect geometric construction of double helix and create the spiral defining golden ratio, the large body like solar system and galaxies are magnificent representation of golden spiral. Sacred geometry is embedded in everything around us.
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“With that in mind, one way to understand the interaction of elements is to see them as sets of triangles crashing into one another and combining to make different sets of triangles.”
The Platonic solids, or regular polyhedra, influence many elements of our environment. They can be found in crystals, the bones of microscopic sea creatures, children’s toys, and art. Many philosophers and scientists have examined them, including Plato, Euclid, and Kepler. They are of significant interest in classical geometry, such as Euclid’s work, which concentrates on the figures themselves. They also play an intriguing role in contemporary geometry, as geometry becomes an application of group theory.
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PLATONIC SOLIDS The Platonic solids, or regular polyhedra, influence many elements of our environment. They can be found in crystals, the bones of microscopic sea creatures, children’s toys, and art. Many philosophers and scientists have examined them, including Plato, Euclid, and Kepler. They are of significant interest in classical geometry, such as Euclid’s work, which concentrates on the figures themselves. They also play an intriguing role in contemporary geometry, as geometry becomes an application of group theory.
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3.2.1 WHAT ARE PLATONIC SOLIDS?
Platonic Solids (Source - daviddarling.info)
The earth has been governed by the most prehistoric philosophy of sankhya.The system of sankhya proposes that all the things that exist on the plane are a mixture of five essential elements. Planets, people, plants and atmospheric particles are all just an amalgamation of earth, water, fire, and air interacting within the ether.
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Earth is the heavy element, the matter of rock and bone, providing solidness and form. Water has the ability to dissolve and it is the ruling form for fluids, including rivers and oceans as well as plasma and mucus. Fire is the element that provides heat and is responsible for all metamorphic processes. Air is the element of movability, carrying concepts, inspiration around the cosmos and human bodies. Ether which we know as "space," It is the vacuum; space through which we move; the 3-dimensional space of matrices in which we arise, live, and transform. The four essential elements dance and intertwine within the ether.
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The interaction of the five essential elements is well expressed by the five regular polyhedra known as the Platonic Solids.The platonic solids are basic building blocks of our fundamental world. In the mathematical world, the Platonic Solids are recognized by "Convex Regular Polyhedra ‘’, where polyhedra categorize as many faces in the Greek language. These are only 5 forms in our 3d dimensional reality, which can be constructed with each face, edge and vertex and angles between each face are identical and perfectly symmetrical in every direction with every side length the same. These well known regular polyhedrons have congruent surfaces formulated of compatible convex regular polygons and have the same number of faces meeting at each vertex. They govern many aspects of our world. They occur in the structure of microscopic atoms, in crystals, in animals and in art as well. These solids were analysed by the ancient Greek philosophers, known as cosmic solids categorized in 5 types. Platonic solids are believed to be representatives of five elements of nature i.e earth, air, fire, water and the universe. They have played an important and interesting role in the geometry of the modern world, where geometry has become an application in everyday life. These 5 different kinds of cosmic polyhedrons are named after the number of faces that each solid has. Plato, who was analysing the platonic solids closely, related each shape with nature. Platonic solids exist with their own unique characteristics that stand them out from the rest All the faces are regular and congruent. Platonic shapes are convex polyhedrons. Faces of platonic solid intersect only at their edges. The same number of faces meet at each vertex. Platonic solids have polygonal faces which are similar in height, form, angles, and edges. Platonic solids are 3-dimensional, convex, and regular solids shapes.
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The platonic solids are also known as regular polyhedrons. They have a very rich history. The origin of platonic solid is still unknown. The polyhedrons all appear in nature right from the crystals to the living beings. The Greek philosopher Plato rediscovered these polyhedrons around 360 B.C. thus they are known as platonic solids. The solids are compared to each of the earth, fire, water, air and elements. The tetrahedron to fire because of the sharp points and edges which depicts stabbing heat from flames. The octahedron was associated with air because division of surface into small smooth parts makes it barely visible which depicts air. He saw an icosahedron as water because it flows out of hands like water. And the cube was associated with earth because it causes dirt to and at the same time it depicts the solidity of earth. The dodecahedron, was considered the shape that surrounds the whole universe and was used for arranging the constellations in the heavens.
Plato The ancient Athenian philosopher Plato rediscovered these unique shapes for the very first time and he considered them as extremely important shapes, hence these solids are known by the name of platonic solids. According to the hearsay, Pythagoras used the platonic solids 200 years earlier before Plato and named them as perfect solids. Plato is convinced by the fact that they are the most basic building blocks of our tangible reality. He stated that nothing would be visible without Fire and nothing would be tangible without Earth. For this motive, He links each platonic solid to the basic elements, or to each state of matter (solid, liquid, gas, plasma). He started with the Cube, which encompasses an exceptionally steady base and is the foremost immovable of all platonic solids. So it compares to the steady Earth or strong matter.
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Plato (Source - aenetworks.com)
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Platonic Solids and 5 elements on the earth (Source - whitman.edu)
The Tetrahedron has the smallest volume for its surface region and so it is the most movable of all the platonic solids. So it compares to the movable FIRE or plasma.The Icosahedron has the largest volume for its surface region and is in this manner the least movable. Other than that, it’s the most spherical looking Platonic Solid, like a bead of water. So WATER, or fluid, is relegated to the Icosahedron. Moreover, in relation to the Tetrahedron, it appears the properties of dryness (fire & small) and wetness (water & enormous). The Octahedron can pivot unreservedly when held by its two inverse vertices. Its volume is between the Tetrahedron and the Icosahedron. It’s subsequently portable and movable. So it compares to the movable Air, or gas. Final remaining one, the Dodecahedron. The dodecahedron compares to the UNIVERSE, or Aether, since the zodiac has 12 signs (the star groupings of stars), compared to the 12 faces of the dodecahedron.
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Kepler In the 16th century, the German astronomer Johannes Kepler attempted to relate the five extraterrestrial planets known at that time to the five Platonic solids. In Mysterium Cosmographicum, published in 1596, Kepler proposed a model of the Solar System in which the five solids were set inside one another and separated by a series of inscribed and circumscribed spheres. Kepler proposed that the distance relationships between the six planets known at that time could be understood in terms of the five Platonic solids enclosed within a sphere that represented the orbit of Saturn. The six spheres each corresponded to one of the planets (Mercury, Venus, Earth, Mars, Jupiter, and Saturn). The solids were ordered with the innermost being the octahedron, followed by the icosahedron, dodecahedron, tetrahedron, and finally the cube, thereby dictating the structure of the solar system and the distance relationships between the planets by the Platonic solids. In the end, Kepler’s original idea had to be abandoned, but out of his research came his three laws of orbital dynamics, the first of which was that the orbits of planets are ellipses rather than circles, changing the course of physics and astronomy. He also discovered the Kepler solids.
Kepler (Source - researchgate.net)
Platonic solids in Sphere (Source - en.wikipedia.org)
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These links that Plato made between the elements and the Platonic Solids has inspired many cultures and other mathematicians. Mainly Johannes Kepler (1571 – 1630) got inspired by the ideas of Plato. He used the Platonic Solids to describe the planetary movements, also known as the Mysterium Cosmographicum. He nested each Platonic Solid inside each other and also encased each of them inside a sphere. Kepler discovered that the spheres could be placed at intervals corresponding to the relative sizes of each planet’s path. With the assumption that the planets circle the Sun.
Kepler Solar System (Source - math.ucr.edu)
So therefore, he assigned the Cube to Saturn, the Tetrahedron to Jupiter, the Dodecahedron to Mars, the Icosahedron to Venus, and the Octahedron to Mercury.
3.2.2 TYPES OF PLATONIC SOLIDS
Sacred geometry works on the principles of the five Platonic Solids: Tetrahedron Hexahedron Octahedron Dodecahedron Icosahedron These are three-dimensional convex forms with congruent faces and corners, each with more angles and faces than the one before it.For example, a tetrahedron with an extra angle becomes a cube, and a cube with an extra angle becomes an octahedron.Each form not only has an additional aspect, but it also fits precisely into the preceding one. As a result, a cube will fit precisely.
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Tetrahedron A tetrahedron is named as a triangular pyramid in geometry. It is organized into four vertices, each with four identical triangular faces, three of which collide. It assumes the shape of a precise triangular-based pyramid that can endure the test of time and the elements.It is considered to be the most "solid" of the platonic solids as a result of this. It is made up of four perfect triangles, a shape that represents unity and is considered the most powerful. It represents the fire element and provides a natural harmony between the physical and spiritual realms. It’s associated with the Solar Plexus Chakra. A pyramid in Egypt, as well as citrine, agates, and hematite, are examples of tetrahedrons . Because fire was believed to have a sharp stinging touch, similar to miniature tetrahedrons interacting with the skin, the tetrahedron was connected with the element of fire. It symbolised manifestation and transformation and had all of the characteristics of fire. There is always one corner of a tetrahedron that prominently points to the sky, no matter how it is rotated. It is the only shape that does not have parallel sides, but instead has fully equal sides leaning on one another, producing the most stable shape possible. It represents determination and provides firm protection from dark and maleficent energies. It enlightens us and opens doors to greater knowledge and consciousness, leading us closer to the Divine. The tetrahedron and pyramid are strong manifestation tools that signify oneness.
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Tetrahedron (Source - en.wikipedia.org)
Tetrahedron and Fire (Source - sacredgeometryshop.com)
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Tetrahedron Characteristics: A Tetrahedron will have four sides (tetrahedron faces), six edges (tetrahedron edges) and 4 corners. All four vertices are equally distant from one another. Three edges intersect at each vertex. It has six symmetry planes. A tetrahedron has no parallel faces, unlike most platonic solids.
Tetrahedron and atomic molecule (Source - sacredgeometryshop.com)
One of the tetrahedron’s points is always at the top, facing the sky. This point represents Source-Consciousness, or the Divine energies that the Spiritus Lumine feeds to all of the other points. In any case, the degree to which all points of energy on the tetrahedron are willing to surrender to Source is the pinnacle of spiritual strength. In energy healing, manifestation, and grid work, the tetrahedron has a wide range of applications. Understanding just how form connects to other metaphysical principles can help understand ideas and put your understanding of life’s essence into better focus. It is also the first of the Platonic Solids, which are a collection of fundamental three dimensional forms that have been analyzed for thousands of years and have helped to develop the foundational mathematics that shapes the universe around us.It also has a bond to the Sun, making it a significant conduit for Light energy, which is one of the ways this form has endless healing potential. Acquiring into a state of balance is a crucial component of any form of healing. In order to do this, this sacred form may be used to assist balance your aura before cleaning. This is because it can stand on any of its faces and still remain stable and balanced. The most common approach to adopt this form for healing and energy focusing is to envisage energy points on the three corners of the base.
Tetrahedron in Merkaba (Source - thebluebudha.com)
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Hexahedron Earth is naturally represented as the hexahedron. Salt crystallises into cubes and is sturdy, making it the foundation of western architecture. Because it has six faces, some people believe it is Tiphareth. Except for the sun, which is positioned in the centre, the six faces naturally suit the sephira and may be connected to the planets. In mathematics, a hexahedron is a solid three-dimensional shape having six square faces, eight vertices, and twelve edges. It’s also a normal hexahedron, according to legend. It’s a solid box-shaped item with six identical square faces, to put it simply. Cubes have a wide range of uses in everyday life as well as in mathematics, making it one of the most significant geometric forms.
Hexahedron (Source - en.wikipedia.org)
The cube is the source of light in the body. This mystical geometric form really defines how spirit interacts with matter, or the body. People often wonder how to bring heaven to earth, according to Metatron. And in many ways, the cube’s fundamental information is that information, since it brings light, heaven, and matter together. It represents the Earth, as well as stability, power, and physical activity. As a result, it was linked to the earth element. It is built on a rock-solid foundation of solidity. For individuals who require patience or a predictable routine in their lives.
Hexahedron and Earth (Source - sacredgeometryshop.com)
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Hexahedron Characteristics: It has a square form to all of its faces. All of the faces or sides are the same size. The right angle is the hexahedron’s plane angle. Each face comes into contact with the other four. There are three faces and three edges on each of the vertices. The edges are parallel and in opposition to one another.
The basis of all things is a hexahedron, which represents a perfect equilibrium between three pairs of squares and is connected with what we perceive in the physical universe. Our most fundamental requirements for protection, persistence, and survival are represented by a cube and a square. It aids in the grounding of our energies and the release of tension when used in a therapeutic process. It is a representation of our physical body, as well as our reasoning, thinking and structure. Hexahedron and Atomic Molecules (Source - sacredgeometryshop.com)
In nature, cubic shapes may be seen in the crystal formation of Pyrite, which is the crystal that assists us in laying foundations and working toward our objectives in an organised manner while also assisting in physical bodily balance. The Root Chakra is associated with the Hexahedron. Grounding energy, sustaining focus, eliminating tension, and alleviating bodily stress are all benefits of meditating with this form. It represents a strong foundation and stability, as well as patience and constancy.
Tetrahedron in nature (Source - hr.bebee.com)
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Octahedron The octahedron shape symbolises the integration of the physical, mental, and spiritual realms, and hence a state of completeness. It is often known as the double Pyramid, and was a crucial component in achieving oneness or enlightenment. It is an Air-form that acknowledges the spiritual physical system’s inter dimensionality. The Octahedron dives into the fourth dimension, which is beyond the three physical dimensions. It’s a time-traveling vehicle, with the past and future coexisting with the present. It generates a matrix for a world with the following basic law: The apparent location (or motion) where the past and future planes of symmetry meet is called the present. The solar energies flowing from the "Atana" (solar sun) to the "Atoms" are also represented by the Octahedron (central sun of earth). It is the "Golden Key" to unlocking all aspects of the cosmic human heart’s timeless loop.
Octahedron (Source - en.wikipedia.org)
The Air element is represented by the Octahedron, which is related to the Heart Chakra, which is the centre for love and compassion. This chakra is where we discover acceptance and forgiveness, as well as our healing and nurturing characteristics. The Octahedron’s self-reflecting form shifts into a higher frequency of introspection, compassion, and healing. We attune to our higher spiritual essence and learn to comprehend our actual nature through working with the Octahedron. Octahedron and Air (Source - sacredgeometryshop.com)
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Octahedron Characteristics: It has eight different faces. An Equilateral Triangle makes up each face. It has a total of 12 edges. There are six vertices (corner points) and four intersecting edges. It is a member of the Platonic Solids.
Octahedron in nature (Source - sacredgeometryshop.com)
The Solar Plexus Chakra is optimally associated with the octahedron, assuring that you are self-assured, determined, and accepting of your actual self. Octahedrons contribute to the harmonizing of the Solar Plexus, allowing you to experience your actual self with the freedom to embrace it with optimism rather than negativity. The octahedron aids in the healing process in our spiritual and emotional selves caused by past trauma. When we’ve damaged ourselves with destructive beliefs, the octahedron can help us bring them to light so we can eradicate them and embrace ourselves completely.
Octahedron and Atomic Molecules (Source - sacredgeometryshop.com)
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The octahedron also encourages selfforgiveness, so that when we recognise our own role in events, we may make apologies and forgive ourselves, removing the need for guilt and shame.
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Dodecahedron The Dodecahedron is the most powerful and flexible of the five perfect polyhedrons or Platonic Solids of sacred geometry that serve as the foundation for atomic, molecular, and cellular life. It has the FA key and the colour green as its matching sound and colour. It is composed of the element ether. Its main qualities are to promote communication, cleanse a room’s energy, magnify intention, and strengthen the chakras. Dodecahedron has twenty vertices and twelve pentagonal faces, three of which intersect. It is associated with our life energy and greater wisdom, making it an ideal form for ascension and meditation. It connects us to the power of all the components that make up reality, assisting us in raising not just our vibration but also the vibration of the area we live in.It is a strong force in helping us detach from the ego and dive into universal truths because of its potential to link us to our higher selves. Because It represents everything unknown and enigmatic, it is utilised to help us tune in to greater knowledge.
Dodecahedron (Source - en.wikipedia.org)
Plato defined the Dodecahedron as a "... god employed for assembling the stars on the entire heaven." Aristotle proposed a fifth element, "ether," and proposed that the skies comprised it. The Dodecahedron represents the Universe (Divine Creation) and is linked to the upper chakras, which hold the energies of meditation, awareness, awakening, higher consciousness, and Spiritual Ascension. Dodecahedron and Ether (Source - sacredgeometryshop.com)
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Dodecahedron Characteristics: 1. A dodecahedron is a polyhedron with 12 pentagonal sides. 2. There are 30 edges on a dodecahedron. 3. It contains 20 vertices (corner points), and three edges intersect at each vertex. 4. It has a total of 160 diagonals. 5. 3 x 108° = 324° is the sum of the angles at each vertex. 6. The angle formed by the sides of a pentagon is 108°, while the angle formed by the intersection of two adjacent faces (Dihedral angle) is 116.56505°. 7. Dodecahedron forms may be seen in a variety of real-life settings, such as the Roman dodecahedron and dodecahedron dice.
Dodecahedron and Atomic Molecules (Source - sacredgeometryshop.com)
The dodecahedron is related with the universe and the sky, and later became associated with Aristotle’s fifth element aether, or spirit, and as a result, the dodecahedron is linked to the fundamental framework of existence. The dodecahedron is linked with the third eye chakra, reminding us of the power of intuition. The paradox is that we would have no knowledge if we did not have imagination. Imagination cannot be formed without information. The fact is that we require both. As we dance between the worlds of heavenly thinking and earthy volition, the third eye fosters both knowledge and creativity. Dodecahedron in nature (Source - sacredgeometryshop.com)
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3.2.3 PLATONIC SOLIDS, SACREDNESS AND SPIRITUALITY
sacred geometry as well as the platonic solids have a positive effect of energies on the human body. Every building block assists in its unique way on a spiritual path helding one thing in common. These building blocks are the most ancient, stable and balanced shapes in the cosmos and balance the energies in the human system and the environment. Platonic solids are linked with basic elements of nature on the basis of energies that they give away. The Tetrahedron resonates with FIRE, the Cube with EARTH, the Octahedron with AIR, the Icosahedron with WATER and the Dodecahedron with the UNIVERSE. Since every platonic solid is linked with one of the basic elements and every basic element also resonates with the chakra of the energy system. Hence the solids have been associated with the energy system. The fundamental framework of sacred geometry formulates the energies of life. These patterns and shapes exist in all living things around us , but they are most visible in nature, such as the delicate patterns of snowflakes, the shapes and forms of crystals, and the intricate arrangement of flowers and pinecones.
Platonic Solids in space (Source - sign.com)
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Platonic Solids and Spirituality (Source - hu.pinterest.com)
The numbers of seeds of life combine to make a flower of life. PLatonic solids are one of the important elements within sacred geometry.there vibrations are associated with awakening and manifestation of the human body. For life to come into existence, there needs to be a healthy seed first to bear that life.Life worships a pattern of Broadening, evolution, existence, and modification . The seed of life is a prolific symbol that helps us conceive thoughts, concepts, emotions and life itself. Independently, each Platonic solid meaning has a specific symbolic story to tell. Sacred geometry assigns symbolic and sacred meanings to certain geometric shapes and certain geometric proportions. These shapes help us to stabilize our emotions and help reach the state of symmetry, which leads to a more fulfilled life. They have multiple dimensions to provide flexibility to fundamental building blocks of life. 2 dimensional shapes like a cube and a square resonate to establish safety, perseverance, and survival.
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GOLDEN SECTION AND FIBONACCI SEQUENCE There is a unique ratio that can be used to explain the proportions of everything in nature, from the tiniest building components, such as atoms, to the most complex patterns in the universe, such as the impossibly massive celestial bodies. Nature relies on this intrinsic proportion to preserve equilibrium, but the financial markets appear to follow suit. In this section, we will look at several technical analysis tools that have been created to take advantage of the pattern. For millennia, mathematicians, physicists, and naturalists have known about the golden ratio. It is based on the Fibonacci sequence, which was named after its Italian creator, Leonardo Fibonacci. Each number in the series is simply the sum of the two preceding numbers (1, 1, 2, 3, 5, 8, 13, etc.).
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3.3.1. GOLDEN SECTION
Golden Section (Source - elegantthemes.com)
One of sacred geometry’s key elements is the golden ratio. This is a completely symmetrical connection between two proportions in which the relationship between the bigger and smaller parts is the same as the relationship between the whole and the larger component. The formula is represented by the Greek letter phi and the equation 1.618. The golden ratio is well-known for creating some of the most beautiful forms. The golden spiral (a logarithmic spiral that becomes wider by a growth factor of the golden ratio) and the golden rectangle are derived from it (a rectangle whose side lengths are in the golden ratio). For centuries, artists and designers have exploited the ratio’s aesthetic harmony, which can be observed in the construction of historic landmarks like the Great Pyramids and the Parthenon. The ratio has been given several various names over the ages, including the golden mean and the golden section.
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Vitruvius man and golden ratio (Source - crl.nitech.ac.jp)
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Golden Ratio in Plants (Source - en.wikipedia.org)
Golden ratio in Universe (Source - kiwihellenist.com)
The Golden Ratio has fascinated the Western world for at least 2,400 years, and it has shaped our idea and perception of beauty over the ages. Architects, musicians, artisans, and sculptors have all based their work on the Divine Proportion throughout history. This "dividing" or"sectioning" property was recognised by the ancient Greeks, a word that was eventually reduced to just "the section." In 1835, 2000 years later the German mathematician Martin Ohm declared both the "ratio" and the "section" to be "golden." The Greeks had also observed that the golden ratio represented the most aesthetically pleasing proportion of the rectangular faces, a concept enhanced in the Renaissance for instance by works by the Italian polymath Leonardo da Vinci, and the publication by the Italian mathematician Luca Pacioli of De divina proportione, which were illustrated by Leonardo. In terms of mathematical features, the Golden Ratio is genuinely unique, and it can be found all throughout nature. The "mathematically challenged" may be more interested in Phi’s manifestations in nature, its use in art, architecture, and design, and its potential for insights into the more spiritual elements of life, but let’s start with the most basic of Phi facts, which can be found in mathematics.
Golden ratio in Animals (Source - quickanddirtytips.com)
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3.3.2. PROPERTIES OF GOLDEN SECTION
The golden ratio may be found in a number of fundamental connections from which many of its features can be deduced. The characteristics of numerical sequences are one of the most fundamental and fascinating manifestations of the golden ratio. An ordered set of numbers created by a well-defined method is known as a numerical sequence. Using one or more seed values and an appropriate recursion relation is one of the easiest ways to generate a number series. The additive sequence is one of the most well-known numerical sequences. The recursion relation is responsible for this, A"+2 = A,+t +An ………………………(Equation1) That is, each phrase is the sum of the two terms before it. A0 and A1 are the two seed values required for this sequence. As an example, consider the situation where A0 = 0 and A1 = 1. This establishes the order, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ..................………………………(Equation 2) Using the recursion relation, this sequence may be prolonged indefinitely. It may also be extended to negative values of the index, n, by applying a recursion relation based on Equation.1 to the values in Equation.2, resulting in a sequence that extends in both directions forever. ………………, 34, -21, 13, -8, 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 8,......................……………(Equation 3) The recursion relation generates another basic numerical sequence known as the geometric sequence.
Golden ratio and Mathematics (Source - medium.com)
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Golden ratio and Geometric Calculations (Source - goldennumber.net)
An+1 =alpha n
.....................………………………(Equation4)
That is, each word is equal to the preceding term multiplied by a constant factor. This sequence may be created with a single seed value and the constant factor value. In a simple example, AO = 1 and a = 2. This results in the well-known sequence of powers of 2. 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ............………………………(Equation 5) It is simple to extend this sequence to negative indices values. ……....………………, 1/32,1/16,1/8,1/4,1/2,1,2,4,8,16,32 ,........................……………(Equation 6) A comparison of Equations 3 and 6 appears to highlight the basic distinctions between additive and geometric sequences. These discrepancies, however, are the result of a specific choice of the multiplicative constant in Equation. Four distinct values for this quantity can provide significantly different effects. The preceding numerical sequence equations demonstrate the connection of the golden ratio to certain fundamental characteristics of numbers. A slightly more geometric approach may provide more insight into the characteristics of the golden ratio. Indeed, it is this occurrence of the golden ratio that accounts for its attraction to ancient thinkers and the origin of its name; the golden ratio.
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3.3.3. FIBONACCI SEQUENCE
The Fibonacci sequence is a well-known mathematical formula. Each number in the series is the sum of the two preceding integers. As a result, the sequence is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. It is described mathematically as Xn+2= Xn+1 + Xn. It’s been termed "nature’s hidden code" and "nature’s universal law," and it’s a fixture of high school and university studies. Everything from the Great Pyramid of Giza to the famous seashell is thought to be governed by it.
Application of Fibonacci Sequence (Source - dreamstime.com)
Fibonacci numbers may be found almost everywhere. This number sequence can be seen in the petals of a flower or in the arrangement of leaves along a stalk. Most flower petals have one of the Fibonacci numbers. The numerals can also be seen in some marine shell formations. These ratios may also be found in parts of the human body, such as the five fingers and a thumb on each hand. Fibonacci may also be observed in a piano, which creates harmony via beautiful music. A piano features a single keyboard with five black keys grouped in groups of two or three, and eight white keys for the 13 chromatic musical octaves.
Fibonacci Sequence in nature (Source - quora.com)
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Leonardo of Pisa, commonly known as Fibonacci, created the sacred geometry pattern that we now know as the Fibonacci sequence in the dark ages of 1202. He followed his father on his trips to North Africa as a child. During this period, he acquired Arabic mathematics. He shared his newfound understanding of this type of algebra all across the world. He discovered this recurring, endless pattern. Since then, this finding has been discovered in nature, mankind, science, math, and even spiritual activities.
Leonardo Fibonacci (Source - thoughtco.com)
Fibonacci method (Source - r-knott.surrey.ac.uk)
Despite his significant contributions to the area of European mathematics, Fibonacci is most recognised for a single sequence of numbers that supplied the answer to a problem published in Liber Abaci. Fibonacci did not create this issue, but his solution to it has made him famous in the mathematical world. The issue, which dealt with rabbit regeneration, estimated the number of rabbits after a year if there is only one couple in the first month. According to the problem, it takes one month for a rabbit couple to develop, and the pair will then generate one pair of rabbits each month after that.According to Fibonacci’s conclusion, there would be just one pair in the first month, one adult pair and one baby pair in the second month, two adult pairs and one baby pair in the third month, and so on. When the total number of rabbits for each month is stated one after the other, it creates the famous Fibonacci sequence of numbers: 1,2, 3,5,8,13,21,34,55,89,144,233,377,........................... SHRAVAN PADATE/FIFTH YR. B.ARCH
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Fibonacci Sequence in nature (Source - pixels.com)
This series of integers is known as the Fibonacci sequence, and each consecutive term is obtained by adding the two prior terms together. The Fibonacci sequence is the earliest known recursive sequence, which is a series in which each next term can only be obtained by performing operations on preceding terms.
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The Renaissance period occurred several hundred years after Fibonacci’s lifetime, when people began to pay more critical attention to the natural world around them. They discovered Fibonacci number patterns in measurements across creation as they investigated the architecture and shapes of numerous plants, animals, and humans. The leaf arrangement on plants, a subject of study known as phyllotaxis, is one place where Fibonacci numbers show consistently. As leaves grow up a plant stem, they form a spiral pattern. Starting with one leaf, let x be the number of spiral turns until reaching a leaf exactly above the first. Let y be the number of leaves met along the spiral between the first and last leaves in this arrangement, excluding the first. This x/y ratio is referred to as the plant’s divergence.
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Fibonacci numbers can also be found in the animal kingdom.This series of numbers, which initially appeared in a problem concerning rabbit regeneration, also appears in the regeneration of other living species. The numbers can be found by inspecting the male bee’s family tree.The spiral that represents animal development is one of the most fascinating occurrences of the Fibonacci sequence in the animal kingdom. The shell of the chambered nautilus has one of the greatest examples of the golden spiral. As the nautilus increases in size, the chamber in which it resides must also grow in size while remaining the same shape. As the shell grows in size, so does the radius of each subsequent chamber, but the angles of contact between each radius and the shell’s outer wall remain constant. This produces chambers that are similar in design but gradually grow in size, resulting in an equiangular spiral with Fibonacci proportions.
Fibonacci Sequence calculation (Source - r-knott.surrey.ac.uk)
This spiral may be seen in many different locations across the animal kingdom, including parrot beaks, elephant tusks, seahorse tails, and bighorn sheep horns. Spider webs, cat claws, the development patterns of numerous seashells, and an insect’s route as it approaches a light source are all examples of spirals. All of these spirals have the essential features of the golden spiral in that they all grow in size while retaining the same form, and the majority of them have Fibonacci proportions in their spirals. This spiral is well known as the golden spiral.
Fibonacci Sequence and geometry (Source - researchgate.net)
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3.3.4. GOLDEN SPIRAL
Fibonacci Sequence in 3rd dimension (Source - semanticscholar.org)
A spiral has traditionally signified limitless expansion, signifying the growth of nature and the world and reflecting the mystical interconnectedness of our micro- and macrocosm. For generations, this knowledge was revered as a means of comprehending life’s inner beauty and spirituality. The Golden Spiral is based on a principle known as the Golden Ratio, which has shaped our sense of balance and proportion over centuries.This golden ratio of 1.618, also known as the Divine Proportion, may be found in almost every aspect of our life, including nature, geometry, the human body, and the planetary system.The Golden Ratio has been known to humans for at least 4,000 years, and maybe even longer! According to some recent study, it was utilised in the design of hieroglyphics found on tomb walls, as well as in the construction of Egyptian pyramids and other ancient monuments across the world. It has been known by various names throughout history, including the Golden Section, Golden Ratio, Golden Mean, and the Magic Ratio, and it is one of the most renowned mathematical formulae. It is a type of built-in numerical system to the universe that is found virtually everywhere in the universe and is frequently referred to as "nature’s secret code."
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The mathematical features of the golden spiral are unique, demonstrating that we live in a universe ruled by mathematical rules. While others feel it is merely a curious coincidence, many scientists and academics believe it is proof of a Master Mathematician or Creator. After all, intelligent design in nature is complicated, and it may appear irrational to some to believe that it occurred by accident. The elegance of the golden spiral has captivated the imaginations of mathematicians, designers, and painters. It may be seen in some of the world’s finest masterpieces of art and architecture. It has also been linked to beauty, since many people feel that beauty is focused on its unique qualities in mathematics and geometry. According to some mystics, the sign will also bring balance and harmony into one’s life. Considering our cosmos is riddled with spirals, it’s no surprise that many people are fascinated by the arithmetic underlying them and their implications. Artists have long regarded the golden spiral as the most visually appealing. It is one of nature’s most inspirational patterns that may be transformed into unique artistic creations. Fibonacci Sequence and Sacred mathematics (Source - newearthknowledge.com)
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3.3.5. PHI
he number phi, also known as the golden ratio, is a mathematical concept that dates back to the time of the ancient Greeks. It, like pi and e, is an irrational number, which means that its terms continue indefinitely after the decimal point without repeating. Over the centuries, a great deal of lore has accumulated around phi, such as the notion that it represents perfect beauty or is found only in nature. Much of that, however, is untrue. The Golden Ratio, Section, or Mean are all based on Phi. Phi has a value of 1.618033988749895. It possesses a number of interesting mathematical characteristics. The Golden ratio is a particular number discovered by splitting a line into two pieces so that the longer portion divided by the smaller part equals the entire length divided by the longer part. It is frequently represented by the letter phi, which is named after the twenty-first letter of the Greek alphabet. The ratio a : a+b is expressed as 1 : 1.618. Phi () recurs endlessly and is also known as dynamic since it is alive in some ways. A golden mean spiral, unlike the Fibonacci spiral, will never be seen or graphed. It may be sensed or experienced in the same way as a vibration or energy field can, but because it is an endless spiral, it is not limited by finite mathematics.
Phi and sacred geometry (Source - youtube.com)
"Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel." -Johannes Kepler
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Phi is named after the great Greek sculptor Phidias (5th century B.C. ), who created towering architectural masterpieces such as Athens’ Parthenon. Certain historians believe that Phidias employed the golden ratio well in his works, according to Mario Livio in his book "The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number." This is why Mark Barr, an American mathematician, chose to commemorate him by giving the sign his initials in Greek (Phi). So Phi was neither discovered by Fibonacci, nor does it bear his name. We learned more about the potential harmonic capability of Phi and its derivatives through mathematics. The Fibonacci sequence and the golden number are two sides of the same coin.
The series discovered by the Pisa mathematician (0,1,1,2,3,5,8,13...) falls within the category of arithmetic . This sequence yields the golden number, symbolised by the Greek letter Phi (,), which indicates the connection between two straight line segments. In other words, Phi is a geometric structure that happens as follows:
Calculation of Phi (Source - interestingengineering.com)
The characteristics of the number Phi are truly surprising, and its exploration as a ratio or proportion led to a thorough evaluation of various forms, objects, illustrations, and even physical movement that occur in our world and are philosophically related to this measurement –the golden ratio or divine proportion.
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“The Golden Number is a mathematical definition of a proportional function which all of nature obeys, whether it be a mollusk shell, the leaves of plants, the proportions of the animal body, the human skeleton, or the ages of growth in man.” — R.A. Schwaller de Lubicz
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SACRED MATHEMATICS Sacred mathematics covered everything of creation in mathematical terms. It contains numerical ratios of great significance, the nature of numbers themselves, their mutual interaction, odd monsters such as Magic Squares and Infinite Series, those amazing features of geometrical relationships in Sacred Geometry that appear to defy logical or reasonable explanation, and the manner in which all of these characteristics explain the cosmos.
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“Geometry is knowledge of the eternally existent. Numbers are the highest degree of knowledge. It is knowledge itself.” - Plato SHRAVAN PADATE/FIFTH YR. B.ARCH
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4.1.1 GOLDEN MATHS
Many spiritual traditions reflect this deeply intellectual interpretation or Mathematical Theory. Such references, however, are not necessarily clear, and may have been purposefully obscured in order to prevent the "uninitiated" from having access to the power contained in such information. The School of Pythagoras, for example, was notorious for limiting the transmission of its mathematical and philosophical understandings. The so-called Mystery Schools of ancient Egypt, Sumeria, Greece, and Judaea were equally concerned with protecting their own secrets and limiting entry to the uninitiated. Sacred Mathematics, on the other hand, is not just concerned with geometry. Magic Squares, Fibonacci Numbers, numbers in general (e.g. Nines), Numerology, and a plethora of other odd correlations among the very real parts of the cosmos are examples.
Phi and sacred geometry (Source - youtube.com)
Pythagoras taught that the Harmony of the Spheres was formed by the motions of the planets, the Moon, and the Sun (as well as an unseen Anti-Earth on the other side of the Sun). Pythagoras thought that each number was sacred and had unique abilities. The indivisible monad created everything from nothing. Two was pure duality, a perfect balance of opposites. The number three represented the gods, whereas the number four represented the earthly world (hence the four elements). This provided the basis for the Numerology that the Order of Hermes eventually embraced. Ancient geometry, like Euclidean and more modern geometries, is based on no a priori assumptions. The origin of ancient geometric philosophy is not a collection of intellectual or abstract concepts, but rather a meditation on the metaphysical Unity. Ancient geometry begins with One, but contemporary geometry begins with Zero. We may describe Golden Math, or Sacred Math, as the mathematics that naturally emerges from the study of Unity. Roman numerals employ a notation akin to Egyptian numeration. Both were based on groups that did not require a zero to signify an empty column. In Roman numerals, for example, 1505=MDV. The ancient Egyptian number progression began with one rather than zero: ......................................................................1/5 ,1/4 , 1/3 , 1/2 , 1 , 2 , 3 , 4 , 5 , ...................................................................
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Many complicated mathematical relationships are hidden in plain sight by geometry. Perhaps the most natural depiction of Unity is the circle. It is sometimes presented with a dot in the centre (the Monad symbol), which relates to the Tao, the essence of all Creation.
Calculation of golden ratio(step 1) (Source - sacredgeometryshop.com)
When you draw two circles, then create multiplicity, just as when you draw a square. The Vesica Piscis sign, two interlaced circles, although not squared, conceals another set of fundamental generative numbers, the square roots of 2, 3, and 5:
Calculation of golden ratio(step 2) (Source - sacredgeometryshop.com)
The Golden Ratio is the final generative number that we must present, and it is probably the most significant. It is the unique technique to divide a unit segment into two pieces by utilising a single integer and its square in geometric proportion:
Formula of golden ratio (Source - en.wikipedia.org)
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"Philosophy is written in this grand book -I mean the universe -Which stands continually open to our gaze. But it cannot be understood Unless one first learns to comprehend the language And interpret the characters in which it is written. It is written in the language of mathematics, And its characters are triangles, circles, and other geometric figures, Without which it is humanly impossible to understand a single word of it." -- Galileo Galilei
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SACRED NUMBER (NUMEROLOGY) Numbers were regarded as a holy science by the Ancient Wisdom systems; they were thought to be the building elements of Life utilised by God to symbolically speak with those who were willing to listen and comprehend. Many ancient peoples, including the Hebrews, Greeks, and Romans, assigned number values to their alphabets and employed words in numerological contexts. Numerology is a pseudoscientific belief in a divine or supernatural link between a number and one or more congruent occurrences. It is also the investigation of the numerical value of letters in words, names, and concepts. It is frequently connected with the paranormal, akin to astrology and divinatory arts.
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Sacred Numerology (Source - sacredgeometryshop.com)
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NUMEROLOGY
It is easier to look at the cosmos as a whole and conclude that it is chaotic. If nothing else, we’ve all heard something about the universe’s entropy. This concept is premised on the theory that in thermodynamics, systems tend to increase in entropy, or disorder. According to such reasoning, the entire cosmos will ultimately reach its own maximum degree of chaos, but it is difficult to explain exactly what that implies. Despite our general concerns about the universe’s logic, a remarkably tiny set of numbers forms the basis for events that occur all around us all the time. The cosmos appears to be more ordered than we realise. Numerology is the study of numbers and how they represent divine energies in an esoteric way. The Egyptians endowed numerals with symbolic value. Numbers’ secret abilities are everlasting, even though their importance fades from time to time. As a starting point, consider the definitions below:
Zero is a verb, an adjective, and a noun all rolled into one. It progresses from being the Prime Mover to signifying a multiplier to becoming a component of a bigger number. Zero denotes pure potentiality (God), and it is the starting point for all other numbers. Even aesthetically, this number represents the egg from which the other numbers hatch. The first prime number is one. It is the process of creation, or genesis. The number two signifies duality and distinction. The yin and yang, the two poles, are represented by light separating from darkness. It’s also linked to the binary system and mitosis. 2 denotes awareness. Two is a feminine number as well (see the vesica pisces). The equilateral triangle—the Holy Trinity—symbolizes masculine number three. It symbolises the union of the head, heart, and stomach. The triquetra, or the rebirth of consciousness, is made up of three parts. This Merkaba represents the union of truth, beauty, and power. The number four signifies stability, the base of a pyramid, the ground, or the earth. It can also refer to the foundation and items associated with order, such as points of the compass, seasons, and the elements: air, fire, water, and earth. The number five represents love. It is represented by the pentagram and may be found in all biological phenomena. It is a cross between the female number two and the male number three.
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Once upon a time, the number six was spelt SEX. This fruitful number is associated with the Flower of Life and the six cardinal directions. It is the number of water molecule points. It also represents the hexagon’s sides. The presence of bees and the buzzing of creation is implied here. The number seven is associated with time measurement: Sirius may be observed rising above the Sun at a height of seven degrees above the Sun. The seventh circle is also the centre of the Flower of Life, a dimensionless space. We have the seven days of creation as God emerges from infinity. Seshat is linked with the number seven, which is a feminine number. POWER is represented by the number eight. It is associated with time and infinity, but it also represents riches and success on Earth: $ is derived from the letter S, which means "eight." It is a representation of the inverted octahedron generating form from spirit. The eight spaces between the ten human fingers represent the musical octave. 8 is a centred heptagonal number as well. The number nine is the final of the cardinal numbers, and it possesses the greatest vibrational frequency of any integer other than the Master Numbers (11, 22 and 33). The number nine is linked with the Hermit tarot card. The hermit, as the term implies, is generally alone in quest of spiritual enlightenment. This number represents the Fibonacci spiral and is known as the number that always returns to itself. Multiples of this number, such as 81, 126, and 1,242, can have their digits added together to confirm this reduction. The number nine is also the number of lighting. Humanity has selected base ten as our counting cycle. It’s simple to understand why with 10 fingers and toes. It symbolises the end of the number cycle or the beginning of the number cycle. The number ten is associated with the Earth and all visible events. The number eleven is connected with spirit, indicating the mirrored adage "as above, so below." The number 11 represents "reflection," and it can give birth to great discoveries. It is susceptible to enormous spiritual notions and the existence of higher forces. 11 is psychically perceptive, channelling its knowledge and meaning from Source. It is personified by Neo in The Matrix and signifies creation or the start of a journey. The number 12 is a higher harmonic of the number three and represents profound insight and wisdom. Except for 2 and 3 (which are factors of 12), all prime numbers appear in just four locations in the base-12 cycle: positions 1, 5, 7, and 11. When those four locations are graphed as a repeating cycle, they combine to produce an exquisite waveform that resembles the doublehelix spiral of DNA. Combining those two overlapping waves yields a single perfect cosine wave, which appears to reflect the basic vibrational chord of the primes and the route along which the vibration of each number finds equilibrium.
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This number represents change. The number 13 is a component of the creation pattern and is also known as 12+1. It is both a Fibonacci and a prime number. 13 is a transformational number that might signify rebirth into a higher state of awareness beyond the Earth plane. The number 13 is linked with Thoth. The number seventeen is associated with the Ankh and immortality. It is reflected in the Sri Yantra’s overt and implicit dimensions. The circle/square harmonic of 17:12 indicates divine awareness. 17 is the link between the folded and unfolded universes. This is the 22nd prime number and the 37th permutable prime. It is also a star number and the prime number with the biggest minimum primitive root among the first 100,000 primes. 73 is also an emirp, which means that its inverse (37) is likewise a prime number. Finally, it is the smallest prime having a base 5 composite total of digits. 144 is interpreted as "God as man" or "man as God." Because 1 + 4 + 4 = 9, this Fibonacci number suggests atonement. As a healing frequency, 144 Hz reveals the creator’s fullness, wholeness, and oneness in all areas of your existence. The sum of its digits is a perfect square (9), the product of its digits is a perfect square (16), and its reverse is likewise a perfect square (441). The Si-O-Si connection that connects two tetrahedra in quartz (like the heart chakra) produces a 144" angle. Light travels at a speed of 144,000 arc minutes per grid second, with a harmonic of 144,000 cycles per second (144 Hz). 432 Hz is still a harmonic of the primary healing frequency (144 x 3). It is known as Verdi’s A, after the great Italian composer Giuseppe Verdi. It stands to reason that singing melodies at 432 Hz would help us feel more balanced because this frequency is simpler to vocalise musically. Finally, most instruments discovered in ancient Egyptian and Greek sites were tuned to A at 432 Hz.
The essence and flow of the energy of numbers fills the cosmos in a cosmic dance creating mathematical equations that bring our thoughts to life. Every single item in the cosmos has a mathematical signature, emitting or toning. Together, these numbers form a symphony that plays throughout the Cosmos, bestowing a beautiful and distinct spiritual vibration and significance on each number and not. Numerology is one of the sacred holistic skills of the earth’s ancient inhabitants. Constellations in the night sky each have a unique set of numbers which are codes giving the instructions of life and the values of placements embedded in the beauty of nature in mathematical formulas that take our breath away and capture our imagination such as the magnificent inspiring beauty of an orchid. This distinguishes each and every event; even a grain of sand is a completely distinct vibration of the occurrences, each expressing the divine in a new and expressive message. The spiritual significance of the numbers provided here is a greater insight into the spiritual potential that each one possesses.
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“Thus nature provides a system for proportioning the growth of plants that satisfies the three canons of architecture. All modules are isotropic and they are related to the whole structure of the plant through self-similar spirals proportioned by the golden mean. - Jay Kappraff
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(3150 BC - 1650 BC) Egyptian Period
Occurence of Sacred Geometry in Different Time Periods (Source - Author)
(559 BC - 331 BC) Islamic Period
(1200 BC - 323 BC) Greek Period
(1200 AD - 1600 AD) Gothic Period
Persian Invassion Alexander invaded North-India and henceforth there was more research towards geometry in architecture
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( 900 BC - 232 BC ) Buddhist Buddhistand andMauryan mauryan Period period ( 900 AD - 1100 AD ) Chandella Periodperiod Chandella
( 1350 AD - 1700 AD ) Vijaynagara VijaynagaraPeriod period Gupta Gupta period Period (400 AD - 800 AD)
Monumental period Mughal Period ( 1000 AD - 1300 AD ) (1400 AD - 1700 AD) Age of enlightment
Mughal Mughal Period period ( 1525 AD - 1761 AD )
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5.1 ANCIENT EGYPTIAN PERIOD(3150 BC - 1650 BC) THE GREAT PYRAMID OF GIZA
Geometry was much more than a study of points, lines, surfaces, and solids, as well as their characteristics and measurement to the Ancient Egyptians. Geometry’s intrinsic harmony was recognised in Ancient Egypt as the most convincing manifestation of a divine design that underpins the world—a metaphysical plan that dictates the physical. Geometry, according to the Ancient Egyptians, was the way by which humanity might comprehend the secrets of divine order. Geometry can be found everywhere in nature: its order underpins the structure of everything, from molecules to galaxies. A design based on holy geometry principles must have the same goal: to use form to serve/represent a function. The majority of ancient Egyptian architecture was massive temple and tomb construction, with obelisks, battered walls, pylon-towers, pyramids, cavetto (or gorge) cornices, huge columns with lotus, papyrus, palm, and other capitals, hypostyle rooms, courts, vast processional axes (called dromos) flanked by sphinxes, stylized sculpture, and hieroglyphs. It was a columnar and trabeated style of building. Egyptian architecture, on the other hand, is well renowned for its pyramids and the geometric principles upon which it is based.
Pyramids have a distinctive geometric form. A pyramid is described in geometry as a polyhedron formed by linking a polygonal base (a two-dimensional structure having three or more straight sides) to a point at the top known as the apex. The Egyptian pyramids may have been inspired by a holy, pointed stone known as the ben-ben. The rays of the Sun were symbolised by the ben-ben stone. A pyramid’s geometric form allows weight to be distributed equally across the building. Giza, near Cairo, is home to the most renowned Egyptian pyramids. Giza’s pyramids are among the biggest buildings ever created. The Great Pyramid of Khufu at Giza is the world’s highest pyramid. View of Giza Pyramids (Source - www.prints-online.com)
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The sacred geometry included into the Giza pyramid is a scaled depiction of the planet, moon, and our own human bodies. The spiral, the golden mean ratio, the triangle, and the square all appear in the Pyramid. The pyramid comprises the number of divinity, three (the 3 sides of each triangle), as well as the number of humans, four ( 4 sides of the square). It depicts the connections between Source and humankind. The Pyramid of Giza in Egypt was constructed to generate energy that allowed people to communicate with the spiritual worlds. The pyramid’s top or peak signifies the pinnacle of spiritual accomplishment, while the body of the structure depicts the ‘journey’ or ascension to enlightenment, swirling upwards. The pyramids were utilised for initiations as well as transportation to ‘other realms.’The initiates used them to go through a type of death and become ‘transformed’ or reborn.’ The merkabah resembles two overlapping pyramids.
EARTH-MOON PYRAMID AND PI RELATIONSHIP
Earth-moon Pyramid and Pi relationship (Source - elementalorgone.co.uk)
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The earth/moon connection is the only one in our solar system that has this one-of-a-kind golden section ratio that "squares the circle." Along with this, the moon and sun appear to be the same size, which is most noticeable during an eclipse. This, too, is only true from Earth’s perspective. This is a claim that no other planet/moon connection in our solar system can make. If the Great Pyramid’s base is equal to the earth’s diameter, the radius of the moon may be calculated by subtracting the earth’s radius from the pyramid’s height. The Earth and Moon have diameters that are 11 to 3 times larger than each other. If the Moon could roll around the Earth, the radius of the circle formed by the moon’s centre is exactly equal to the perimeter of a square around the Earth. That is, the Earth and Moon’s sizes indicate a "squared circle" connection, a beautiful marriage of impossibilities: circle and square, irrational and logical, Heaven and Earth.
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Encoding Phi- 1: 1.618 (Source - scontent.fbom)
golden spiral is formed by successive points splitting a golden rectangle into squares on a logarithmic spiral. The ‘Golden Mean Spiral,’ formed from the ‘Golden Ratio,’ is one of the most deep and significant activities contained within sacred geometry and light Source. The phi ratio may be found in the Great Pyramid’s construction in the triangle created by the height, half-base, and the apothem, or diagonal. The Golden Section is demonstrated by the structure’s fundamental cross – section. If the half – base is set to 1, the apothem is equal to phi, and the height is equal to the square root of phi. The Golden Section appears often in Giza.
Planning with Golden ratio (Source - alchemisoul.tumblr.com)
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5.2 ANCIENT GREEK PERIOD(1200BC - 323 BC) THE PARTHENON
The Parthenon is a temple dedicated to the Greek goddess Athena that was erected on the Athenian Acropolis in the 5th century BC. The golden ratio and its aesthetic characteristics are said to have been known to Phidias, the principal Greek artist in charge of adorning the Parthenon. In fact, Phidias inspired the Greek sign for the Golden Ratio, Phi . The golden rectangle, a rectangle whose length to breadth ratio is the Golden Ratio and is said to be the most pleasant to the eye, is nearly omnipresent throughout the Parthenon’s façade and floor layouts. A golden rectangle may encircle the entire façade. The golden ratio is also the proportion of the length of a metope and triglyph to the height of the frieze, as well as the proportion of the height of the columns and stylobate to the total height of the temple. The Parthenon is the best example of how "successful accomplishment in art is the consequence of precise consistency in a number of arithmetical proportions." Every esoteric researcher diving into the depths of "divine proportion" or "golden mean" cites the Parthenon as his first example: it has never failed to satisfy millions of eyes, and it measures out to a mathematical formula. There is determined proportioning of components and rhythmic correspondences across the entire aspect.
Incorporation of golden ratio in elevation (Source - plus.maths.org)
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The grid lines appear to illustrate golden ratio proportions in these design elements: Column height – The structural beam on top of the columns is proportional to the column height in a golden ratio. Each grid line is a golden ratio proportion of the one above it, thus the third golden ratio grid line from bottom to top at the base of the support beam indicates a length of phi cubed, 0.236, from the top of the beam to the base of the column. Dividing line of the root support beam - The structural beam on top of the columns has a horizontal dividing line that is proportional to the height of the support beam in the golden ratio. Column width – The column width is determined by a golden ratio proportion produced by the distance between the centre line of the columns and the outside of the columns.
Proportions of structure with golden ratio (Source - mathematicsmagazine.com)
Each of these golden ratio proportions is extremely close to flawless, but perhaps not as accurate as one might think, especially considering the precision of the Parthenon’s design and construction. the golden ratio proportions found in the height of the roof support beam and the ornamental rectangular pieces running horizontally across it The gold grids below are golden rectangles with a width to height ratio of exactly 1.618 to 1. golden ratio rectangle that appears in the design work above the columns. This, probably more than any other single feature of the Parthenon, provides rather compelling evidence that the Greeks knew of, and applied, the golden ratio in the construction of the Parthenon.
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5.3 GOTHIC PERIOD (1200AD - 1600AD) NOTRE-DAME CATHEDRAL, PARIS
View of Notre Dame Cathedral (Source - pickyourtrail.com)
Notre-Dame Cathedral is a Parisian cathedral church. It is the most well-known Gothic cathedral of the Middle Ages, notable for its size, history, and architectural appeal. The originator of Gothic style, Abbot Suger, was a disciple of the School of Chartres, and it was through this school that St. Augustine’s Neo-Platonism dominated the designs of Gothic churches in France. According to St. Augustinian’s beliefs, "the goal of geometry was to purify the structure by making it part of the celestial universe of God ‘’ (Dudley, 2001). As a result, the spiritual architecture of mediaeval cathedrals was regulated by two laws, both of which contribute to the notion of connecting the structure with celestial geometry: The first rule is Euclid’s Ad Quadratum, or square in circle, which was developed by theologians of the time into squaring the circle (Hendrix, 2003), making an analogy in which the square represents the Earth’s limited space, whereas the circle, which has no beginning and no end and is the source-figure from which all other geometrical shapes emerge, represents the boundlessness of the Heavens (Lundy, 2001). The second requirement was to be consistent with Nature’s geometry. This rule arose from the Augustinian view that the universe’s stability is due to the Creator’s perfect balance of its constituents. It was therefore necessary for the geometry of a structure to be connected with and serve as an extension of the geometry of the cosmos.
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Several mediaeval symbols can also be realised by examining the plan’s essential points. The plan is divided into five sections: the chevet, choir, transept, nave/aisles, and narthex. In Neo-Platonic theology, the number five had a dual meaning. It connotes the stigmata, a protective emblem, while its geometric representation, the pentagram, is a divine proportions symbol (human body and Golden Section). It is also the product of 4 + 1. (the Matter and the Divine). To find the crossing critical points, the plan extensively utilises the geometric concepts of Ad Quadratum, Vesica Piscis, Sacred Cut, and pentagram.
Tree of Life incorporating in plan (Source - sciencedirect.com)
This floor plan’s geometric design is based on "dynamically unfolding geometrical processes" (Bork, 2014), in which "geometry offers a quasi-random growth factor in reference to eternal expansion." The general ground layout is based on a Vesica Piscis with two pentagrams, the points of which correspond to the so-called Light Matrix, where it was believed that Spirit (light) and Matte (man) met. Another symbolic figure in the design is the Sephiroth, often known as the Tree of Life. This sign was thought to have divine power in mediaeval literature. The dimensions of the human body (divine proportions) are also apparent in the plan’s design.
Plan and Relation with human body (Source - sciencedirect.com)
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The west front is an imposing, simple mass whose grandeur is built on the interaction of vertical and horizontal lines (Heaven and Earth): four strong buttresses spring up to the tops of the towers, raising them heavenwards, while two wide horizontal stripes appear to pull the structure back down to mortal Earth, dividing the squared base of the façade into four worlds. By superimposing the west facade layout above the ground plan scheme, a substantial correlation between them can be noticed, referring to the correspondence between horizontal and vertical levels (Heaven and Earth). This facade is one of the most wellknown examples of the use of the Golden Ratio. It was defined by Le Corbusier as a “pure invention of the spirit, governed by the circle and the square” (OSNDP, 2020.) and so is also the plan.
Golden Ratio in elevation (Source - notre-dame-de-paris.net)
The geometry of this facade is similarly dominated by Vesica Piscis. The entire bulk of the facade might be represented by two vertical Vesica Piscis circles, one descending from Heaven and the other rising from Earth (Schneider, 1995). The portals have a similar geometric layout, but the doorway’s two circles are horizontal.
Openings and Vesica Picsis (Source - notre-dame-de-paris.net)
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This floor plan’s geometric design is based The angle at the base of the triangle connecting the Rose Window and the portals is 52°, which is extremely similar to the angle at the base of the Pyramid of Cheops (51° 51 ). (Hale, 1995). Another "pyramid" can be discovered by connecting the ends of the Galerie des Chimères with the point in the middle of the horizontal line connecting the two towers . The Pyramid here represents “certain spiritual aspects, as the earliest and most well-known symbol of squaring the circle,” with “the eye of God opening” at the summit of the pyramidal shape (Campbell, 1988). The interior timber structure of the roof is likewise inclined at 52°. (Bruzelius, 1987).
The massive Rose Window is the most noticeable element of each of the side fronts. Rose window geometry is one of the most powerful uses of squaring the circle. The design of the side Rose Windows, like that of the West Rose Window, is reminiscent of the Hierarchies of the Universe. It also seems to be a radiant star, which is a sign of direction.
(Source - sciencedirect.com)
3D Rendering of the project (Source - sciencedirect.com)
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5.4 AGE OF ENLIGHTENMENT (1400AD - 1700AD)
Classical architecture was revived in the 18th and early 19th century as Neoclassical architecture. Unlike Classical revivalism, which tvended to reuse Classical pieces, the movement was concerned with the logic of whole Classical books. Neoclassical architecture is distinguished by grandiosity of scale, geometric simplicity, Greek—particularly Doric—or Roman detail, dramatic use of columns, and a penchant for blank walls. The new desire for ancient simplicity was a reaction to the excesses of the Rococo style.
CITY PLANNING OF WASHINGTON D.C.
3D Rendering of the project (Source - cnu.org)
Pierre Charles L’Enfant, who immigrated to America from France to fight in the Revolutionary War and climbed from obscurity to become George Washington’s trusted city designer, is renowned for most of Washington, D.C.’s unique design. L’Enfant envisioned a great capital with broad avenues, public squares, and inspirational structures amid what was then an area of hills, woods, marshes, and plantations when he designed the city from the initial concept.
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L’Enfant picked Jenkin’s Hill as his starting point since it has the greatest height in the area; this is now known as Capitol Hill. This makes the Capitol Building the focal focus, rather than the White House. This site metaphorically symbolised the citizen’s prominent role in the new democracy. Two streets branch out from this centre location, one heading north-south and the other eastwest. The ancient Romans, who utilised a central point to build the Cardo, the major thoroughfare running north-south, and its companion known as the Decamanus, which ran east-west.
City planning (step 1) (Source - cnu.org)
L’Enfant picked Jenkin’s Hill as his starting point since it has the greatest height in the area; this is now known as Capitol Hill. This makes the Capitol Building the focal focus, rather than the White House. This site metaphorically symbolised the citizen’s prominent role in the new democracy. Two streets branch out from this centre location, one heading north-south and the other eastwest. The ancient Romans, who utilised a central point to build the Cardo, the major thoroughfare running north-south, and its companion known as the Decamanus, which ran east-west.
City planning (step 2) (Source - cnu.org)
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A pentacle is formed by dividing a circle into five equal-sized pieces. L’Enfant then split his circles in this manner, resulting in pentacles within each, with points pointing east. In ancient cosmology, the number five, represented by the pentacle, signified the earth and its people. This was employed by L’Enfant to depict the citizens as represented by the Capitol Building. The alignment of avenues is determined by the angled sides of the stars.
City planning (step 3) (Source - cnu.org)
Plenty of cascading stars appear. The Golden Section, which emerges from the star alignment, dictated the sites of significant buildings, public spaces, and so on. This design serves as the city’s conceptual master plan. Avenues radiate out from the White House utilising a distinct set of geometric concepts. L’Enfant utilised a 60-degree angle to connect two avenues, Vermont and Connecticut Avenues, which create an equilateral triangle. A circle may be cut into six equal pieces. This produces a hexagram, which when connected together forms the basis of the Flower of Life design. The reason for L’Enfant’s change to this other layout on the city’s western outskirts.
City planning (step 4) (Source - cnu.org)
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The grid system, which is based on a pattern of cascading stars, came last. The alignment of the star points and the edges determined the importance of some routes, such as 8th Street, which runs halfway to the White House. The huge grid that resulted was subsequently subdivided by quarters or eighths, resulting in the syncopated grid layout mentioned previously. Thus, the avenues are not simply superimposed on top of the grid; rather, the grid arises from the angles, points, and intersections of the star pattern.
City planning (step 5) (Source - cnu.org)
View of Washington City (Source -thoughtco.com)
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City planning (step 6) (Source - cnu.org)
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5.5 PERSIAN AND ISLAMIC PERIOD (700AD - 1800AD) SHAH-MOSQUE IN ISFAHAN
The Shah-mosque is the most significant historical mosque in Isfahan, erected on the instructions of Shah Abbas I during the Safavid dynasty. Its construction began in 1611 and was finished in 1629. It was designed by Ali Akbar Isfahani, one of Iran’s most famous architects. This structure symbolises the pinnacle of a thousand years of mosque construction in Iran. This mosque’s bulky components and embellishments are stunning and wonderfully fitted together, making it one of the greatest in the world.
In the plan, there are six golden rectangles to be found. These rectangles were chosen because of their intrinsic dimensions. The main golden rectangle is associated with the eastern portion. The golden rectangle demonstrates that golden distances remain on the plan’s major lines, and the centre point aligns with the altar. The red circles represent significant places of intersection between the plan and the analysis.
Plans incorporating golden rectangle (Source - degruyter.com)
The golden rectangle is considered horizontal and is located in the north section of the design. It demonstrates that golden lengths divide all of the plan’s key lines. The northern rectangle’s dimensions are virtually identical to those of the eastern rectangle. The most significant line between the building and the yard is divided by golden proportion, and the midway on the left-hand side remains on the building’s main entrance. These modifications are well-organized. Because of the plan’s symmetry, the southern half may receive comparable analyses.
Plans incorporating golden rectangle (Source - degruyter.com)
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The golden ratio has divided two sides of the main porch from the yard. It indicates that the primary walls are at golden distances. Two additional connections remain on the smaller southern porch’s centres (entrance and dome). This rectangle is located in the centre and extends along the main entrance in the plan’s turning. Two golden centre lines in the right image correspond to the entry and main porch walls. Furthermore, they intersect along the pool’s borders. There is a connection at the main entryway of the main dome and two more junctions in the perimeter of two large hallways in the midway of the golden rectangle’s phi side.
Incorporation of golden ratio in section (Source - degruyter.com)
The section demonstrates the existence of the golden ratio in this structure at an exceptional extent. The main dome portion is represented by two golden crossover rectangles. It is placed on the dome’s curvature point and extends from the tip. The horizontal rectangle has been split into two equal halves. The dome arc is nearly parallel to the golden spiral arc, and the beginning point of the finial-head is separated by the golden ratio.
Incorporation of golden ratio in section (Source - degruyter.com)
The smaller portion of this cut is also entirely contained inside the golden rectangle. The major lines separating the spaces and the roof are likewise separated by golden lines. Furthermore, the final point is located towards the centre of the smaller dome. Sacred geometry may be the only science that connects engineering, aesthetics, and symbolic elements. When the aesthetic and technical aspects of an architectural work interact with one another and neither dimension dominates the others, the work is in its optimal condition. The golden ratio is prominent in the mosque’s plan, section, exterior, and ornamentation.
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5.6 INDIAN ARCHITECTURE MOURYAN PERIOD AND BUDDHIST ARCHITECTURE (900 BC - 232 BC) SANCHI STUPA , ROCK-CUT ARCHITECTURE
The Great Stupa at Sanchi in central India was one of the first stupas, serving as an architectural model for all that followed. The world-famous stupa, built in brick by the Mauryan king Ashoka in the third century BCE, was later enlarged in stone to twice its original size. In the most basic sense, a sacred stupa, no matter where it is in the globe or when it was erected, has three essential characteristics.
A hemispherical mound (anda)The domed shape of the anda (green accents) evokes a mound of earth used to bury the Buddha’s corpse. It has a strong core and cannot be penetrated, as one might anticipate. This hemispherical mound has taken on a wider metaphorical significance over time: the mountain abode of the gods at the heart of the cosmos. A railing that is square (harmika) The harmika (red accents) is inspired by a square railing or fence that surrounded a mound of earth, designating it as a holy burial ground. Enclosure wall with ornamental gates (toranas) in four cardinal directions The wall encircles the whole house and is distinguished by three horizontal stone bars (seen in the top image). The wall is highlighted in light blue, while the toranas are highlighted in yellow. Sanchi Stupa and the use of Sacred Geometry (Source - ritiriwaz.com, in.pinterest.com, Edit - Author)
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INDIAN ARCHITECTURE (900 BC- 1700 AD)
Gupta Dynasty (Source - silentpagesindia.blogspot.com)
Monumental Temple (Source - freepressjournal.in)
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Chandella Dynasty (Source - tripoto.com)
Vijaynagara Dynasty (Source - gosahin.com)
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KANDARIYA MAHADEV TEMPLE, KHAJURAHO
The Kandariya Mahadev temple at Khajuraho is considered to be the pinnacle of Hindu art in India. This temple was built in the middle of the 11th century, when Hindu temples had reached their pinnacle of design maturity. Sculpture, music, and dance, among other forms of Hindu art, were incorporated into temple designs at this time. The Kandariya Mahadev temple stands at a height of roughly 31 metres. The temple construction is sanctified and magnificent because it is elevated atop a towering plinth. The construction is 30.5 metres long and 20 metres wide, and it faces east to catch the first rays of the sun. View of the Temple (Source - d-lab.kr)
Elevations of the Kandariya Mahadev Temple (Source - d-lab.kr)
Kandariya Mahadev temple is distinguished from other temples in the vicinity by its enormous scale, intricate construction design, and adornment. The vertical visual rhythm is created by the temple’s well-controlled zigzag design, which is reinforced in the elevation by its acute recessions and projections, whilst the horizontal rhythmic expansion upward is created by the elevation’s horizontal friezes. The temple’s most distinguishing feature is its tall curving rises above the sanctuary. It is referred to as shikhara. The shikhara is capped by an amalaka, a ribbed circular design, and a pot finial known as the kalasha, a holy pot in which the most valuable elixir amrita was kept. SHRAVAN PADATE/FIFTH YR. B.ARCH
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Fratal dimension is a quantity in fractal geometry that gauges an object’s fractalness. Fractal dimension is always non-integer for every fractal item; fractal object is a fractional-dimensional object that can be between one and two dimensions, or between two and three dimensions. The fractal dimension measured by the ‘box counting method’ evaluates an image’s fractalness based on roughness, texture, or the number of features. The planning of the temple is based on the grid of circles which after connecting the lines forms a fractal pattern of repetitive geometry on the exterior of the temple.
Fractal Planning (Image Source - d-lab.kr, Edit - Author)
The ‘Box-Counting Demonstration’ software, for example, counts marked boxes by taking the box sizes or grid sizes 24, 12, 6, and 3 of a squares grid for a fractal picture of 60 mm 43:5 mm with resolution 80 pixels/cm. Then, using the log of grid sizes (S) on the X-axis and the log of marked boxes (N) on the Y-axis, the following results are obtained. The slope of the resulting line in the log–log graph indicates that the image’s fractal dimension is 1.55. The resultant dots on the graph, which lie on a smooth straight line, reflect the homogeneity of visual features at different sizes. Fractal dimension 1.55 reveals that the fractal picture has a medium amount of detail. Box Method Calculations (Source - d-lab.kr)
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The garbha griha, mukhya sabha mandapa, sabha mandapa are based on golden squares and are in proportion to each other and the exterior follows the golden section. One smaller square within the grid of the mandala, one pada, has been considered as one unit in this geometric procedure. The outward forces created from the mandala’s core have pushed the centre of each side up one unit along the four directions. Then, from the quarter of a pada, all of the newly born outside corners have been filled with meandering parts. Each meandering piece is made up of a golden rectangle and a square that grew from the same rectangle. After filling in the outer corners, it has a fractal design that is overlapped with a self-similar pattern intended for the mandapa along the axis of the sanctuary’s entry.
Planning on the basis of Golden Rectangles (Source - d-lab.kr)
Analysing Kandariya Temple Geometry wiht Box method (Source - d-lab.kr)
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Proportion of Shikharas (Source - d-lab.kr)
The beauty of shikhara is hidden beneath the dimensions of the imitation arrangement. The repeats of the towers in Hindu temples are not done haphazardly, but rather according to particular standards and proportions for the benefit of society and the cosmos. Its dimensions are extremely important, since if the temple is built correctly according to the mathematical system, it will be able to work in accordance with the mathematical foundation of the cosmos. Almost every Hindu temple in North India follows the same tower repetition guideline. The stratification of the towers above the sanctuary appears to follow the golden ratio as the fundamental basis for layout. The peaks of the first, third, and fifth towers all follow the golden ratio, with the distance between the first and third tower peaks determining the squares of the third and fifth towers.
Carvings of natural objects (Source - d-lab.kr)
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6.1. SACRED GEOMETRY AND SYSTEM OF BALANCE IN NATURE
Spiral of Galaxy (Source - space.com)
Dual Helix in DNA (Source - businessinsider.in)
There is a geometry to both physical existence and energy existence. Because of geometric perfection, everything in the cosmos, from the atomic to the cosmic, operates the way it does. A triangle is one of the most fundamental and stable structures in geometry. In the human energy system, there are two equilateral triangles — one pointing upward and one pointing downward.
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Platonic Solids (Source - sacredgeometryshop.com)
Basic Forms in Nature (Source - joy-pup.com)
Balance is achieved through sacred geometry. Male and female energy coexist. Male energy is related with the left side of the brain, which 90 percent of the population resonates with more, and male and female energy are not synonymous. Along with energy, this side of the brain is practical, linear, rational, and statistical. Female energy, on the other hand, is passionate, creative, curved, and emotional. This energy is compatible with the right side of the brain. Female energy considers wholes, whereas male energy considers pieces.
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6.2. SACRED FORMS- ENERGY AND VIBRATIONS
There is no such thing as solid matter in the Universe. A solid shape is generated by underlying vibrations that manifest themselves in matching geometric patterns and figures that build larger and larger parts that eventually combine to form diverse types of solid matter that we can perceive with our eyes. Sacred geometric forms lead us back to our original nature, allowing us to connect more profoundly to the inner and harmonize with the outer. It broadens and links us on several levels. Each geometric form has its own energy frequency, intention, and energy sensation. When used in meditation or healing, they can cause an energy change in your being and awareness, resulting in healing and rebalancing.
Relation of Sacred forms and souls (Source - fractalenlightenment.com)
According to quantum physics, which studies the Universe’s tiniest building pieces, everything is made up of energy, including our thoughts and feelings, and that energy vibrates at different frequencies. These distinct vibrations may now be measured by quantum physicists. Negative emotions with lower vibrations include pain, fear, and fury, whereas good emotions with higher vibrations include love, joy, and liberation.
Energies of Atomic Particles (Source - eandt.theiet.org)
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Sacred forms also reflect the ethereal, mystical aspects of life. Why else would we be so drawn to them? Is sacred geometry linked to anything deeper within our collective consciousness? Does it reflect or address the language of the soul? Or are our brains just programmed to perceive natural patterns? Whatever the explanation for the ubiquity of these patterns, one thing is certain: symbols have power. Here are some geometrical patterns to assist you connect your body and soul to the holy language of the cosmos.
Triangle The platonic solids are regarded as the sacred geometry ‘building blocks’ of the Universe, as taught in Greek Mystery Schools 2,500 years ago. The triangle, on the other hand, is a symbol that underpins all of them. Triangle represents balance, harmony, and fulfilment. Rising upwards, it raises us to a higher level of consciousness and it helps to clarify the mind.
Energies of a Triangle (Source - slunecnabrana.eu)
Metatron’s Cube
Aura of Metratron’s Cube (Source - evolutionaryascension.com)
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Metatron’s cube can be used to eliminate lower vibrational energies, balance and activate chakras, raise vibration, and so on. Metatron’s cube and other geometric light formations help to remove and discharge dense energy, poisons, and negativity in any form as they spiral through your mental, emotional, physical, and spiritual bodies. Metatron spins various spiritual forms, including Metatron’s cube, through your chakras and all levels of your existence to emit energy. The upper triangle represents masculinity, while the descending triangle represents femininity, with the two combining in perfect harmony.
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Spiral The phrase ‘as above, so below’ connects heaven and earth. The spiral’spirals’ up to connect the physical self to the Higher Self and all levels of our being (interdimensionally), as well as into the centre of the Earth. Galaxies are engulfed in energy spirals. Spirals of energy move. The spiral is also the kundalini, which represents rising one’s awareness on the path of soul growth. The spiral represents the movement of energy through the chakras as they rotate in a circle. The spiral is the spiral form as a double helix in each cell’s DNA. Spiral connecting soul to universe (Source - shambali.com)
Merkaba The Merkaba is all about finding a happy medium. This delicate and precious star balances our being by repairing and kindling the activity on both sides of our brain. By activating both sides of the brain, we may tune in deeper, get a better knowledge, and open ourselves up to new spiritual paths. The Merkaba’s energy may cleanse sluggish and negative energy while also stimulating a new flow. This may enlighten us from head to toe, as well as make us feel more connected, aligned, and at one with our actual aspirations. With that new surge of energy comes a sense of delight and refreshment.
Energies of Merkaba (Source - dreamstime.com)
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The shapes and forms found in nature are built in a way to radiate energies and vibrations. With the changing energy and vibration, these forms gain specific spiritual significance. By changing the frequency of energies, matter also tries to change its pattern to balance itself.
Changing form with changing frequencies (Source - pinterest.com)
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6.3. INFLUENCE OF SACRED GEOMETRY ON PERSON
Sacred geometry amplifies our connection to the spirit, and creates harmony within ourselves,and between ourselves and the outside world. These patterns are symbolic of our own inner realm and are significant to higher consciousness and selfawareness. Sacred geometry brings about certain effects of healing, harmonizing and rebalancing on all levels. It connects the inner and outer self, uniting all. Sacred geometry refers to the manner in which forms and patterns appear in nature, including the mental and spiritual realms. A thorough examination of these patterns exposes the numerous ways in which we are linked at all levels of existence. Sacred geometry may be proven to have a correlate with any discipline or manner of knowing. Even mathematics would be impossible without sacred geometry, because numbers and their rules emerge from shape, form, proportion, and the links shown by these.
Seven Chakras and Sacred Geometry (Source - musicenergetics.net)
Their significance stems from their enormous creative capacity. In the abstract symbolism of geometry, these structures depict the points at where the „universes“ of the left and right cerebral hemispheres collide. Even on a physical level, the act of changing the linear into the holistic is incredibly creative, with transformational spiritual effects.
Meditation and Sacredness (Source - thriveglobal.com)
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Vitruvius Man and Sacred Geometry (Source - sw-ke.facebook.com)
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Source - twitter.com
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1. MATRI MANDIR, AUROVILLE, PONDICHERRY
The Matrimandir is also called the “House of the Divine Mother”. Its purpose is to realize human unity and the transformation of consciousness, ushering in the great awakening of the new age. It reflects Sri Aurobindo’s model of multi-dimensional reality, of the universe, which describes the system of Integral Yoga in the The Life Divine.
Planning of Auroville Source - auroville.org, twitter.com
Existence, Consciousness, Bliss, Light, Life, Power, Wealth, Utility, Progress, Youth, Harmony, and Perfection are the names given by the Mother to the 12 Main Gardens around the Matrimandir. Matrimandir now receives over 800,000 tourists each year. The Matrimandir gardens are intended to be a location where one may discover and explore various levels of awareness while surrounded by a beautiful scenery. As they walk from one garden to another, the visitor can experience the state of awareness of that garden and transition from one conscious experience to another.
For the human consciousness, the circular movement or connectivity in the gardens begins with the involution of ExistenceConsciousness-Bliss (Sat-Chit-Ananda) and goes upward from Light-Life-Power to the last garden, Perfection.
Planning of Matrimandir Source - auroville.org
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Consciousness is the spiritual basis of nature’s multidimensional reality and seven lokas of the Vedic Puranas and is known as the plane of consciousness. The Great Pyramid triangle as the mediating geometry between the circle and the square, Spirit and Matter, and having golden proportions, is a central teaching in sacred geometry.
Figures of Sacred Geometry in MatriMandir (Source - mind-matrix.net)
The globe’s construction is a precast concrete space frame supported off the ground by four concrete piers depicting the Divine Mother’s four aspects or personalities: Kali-power, Lakshmi-beauty, Saraswati-perfection, and Shwari-wisdom and compassion. It is encased in round laminated gold discs that are positioned off the outside surface to allow air to pass behind them and cool the structure. Staircases lead from the four piers to the entry level, where two spiral stairs continue up to an intermediate level.
Matrimandir and Cosmology (Source - mind-matrix.net)
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The Inner Chamber measurements generate a triangle that is identical to the Egyptian Great Pyramid of Gizeh. The chamber in the centre of matri mandir is built on the concept of the seed of life and with change in geometry, the light quality as well as spatial quality of space changes. This identical triangle is the key to Circling the Square, a sacred geometry diagram in which the height of the triangle is the radius of the circle, which is equivalent to the square with a side equal to the triangle’s base. As a result, the diameter of the circle, which represents Spirit, is equivalent to the perimeter of the square, which represents the Body or matter. Floor Plan at the Inner Chamber (Source - mind-matrix.net)
Internal Spaces of the Matrimandir (Source - mind-matrix.net)
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Source - tripadvisor.in
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2. QUIET HEALING CENTRE, PONDICHERRY
Quiet Healing Centre is an instance of a paradigm, or the progression of a process. The institution is located on a seven-acre beachfront estate and offers a wide range of natural therapeutic therapies in the tranquil natural settings of Auroville. The word Quiet represents the concept of creating a space where individuals who are stressed out by their everyday lives may come to recover and revitalise.
Site Plan of Quiet Healing Centre (Source - pdfcoffee.com)
The location is on the shores of the Bay of Bengal, which is advantageous for a therapeutic environment. The entrance to the property, which borders the sea, is densely forested with palms and native flora. The availability of landscaping courtyards linked with rock gardens gives the built-form an unprecedented feeling of openness, functioning as localised healing grounds for people. SHRAVAN PADATE/FIFTH YR. B.ARCH
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Quiet’s healing work is based on the understanding that a person is first and foremost a spiritual being seeking to express its truth through the use of the mental, vital, and physical natures. Disharmonies emerge when the more or less uninformed instruments distort the energies attempting to manifest through them, and these disharmonies are what we identify as sickness. Each therapy respects and aims to operate in tandem with the body’s innate knowledge. Each therapist sees himself as a lowly instrument of the indwelling Spirit, who is ultimately the sole Healer.
3D Rendering of the project (Source - Nasa India NG Trophy 2012 LSRSA)
The hydrotherapy area is designed in an organic-free-flowing style that connects all of the consultation rooms with planted walkways that use geometry to accurately establish scale and proportions. To avoid the usage of concrete, the architect mounted the panoramas using pre-cast rings, complementing the architectural features in a unique way.
Project Plan (Source - Nasa India NG Trophy 2012 LSRSA)
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Impact of the Dome on a Human (Source - Nasa India NG Trophy 2012 LSRSA)
Healing centre consists of domes named as healing spheres. The incorporation of natural light into the domed therapy/consultation rooms, as well as the use of local brick, lime mortar, and bio concrete, exemplify his idea of building in harmony with nature. According to bau-biologie circular form has zero energy in the centre. Hence these rooms are cylindrical. Height of the dome is lessened so that the user feels comfortable and at ease.
Sectional Elevation (Source - Nasa India NG Trophy 2012 LSRSA)
The buttresses have circular fenestrations large enough to accommodate a person, breaking his vision of the scenery and making him concentrate on line of thoughts. The triangular shaped buttresses makes the person feel secure - like in the arm of the mother. Using large windows on the east façade, both round and rectangular, allows breathtaking views of the beach while lowering radiation in the interiors and providing a wave of serenity and quiet to the environment.
View of the buttress (Source - Nasa India NG Trophy 2012 LSRSA)
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1. SITE SELECTION Site selection has been done on basis of following criteria-
The Isolating from the city
The site and nature Source - Author
Source - dreamstime.com
The site should be surrounded by nature
It should be in a part of the city which is easily accessible but is also detached from the fast pace of the city.
Dense population
Adjoining Waterbody
Source - dreamstime.com
Source - rairiegardentrust.org
Site should be located in a densely populated area.
Site may have a water body near which could help in healing agitation due to its therapeutic quality.
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The shortlisted potential sites are in Kochi, Mumbai and Chennai.
Shortlisted sites Source - researchgate.net
Willingdon island, Kochi Source - google.co.in/maps
This site is on Willingdon Island in Kochi. It is surrounded by water on three sides, is connected by two highways, and serves the dense populations of Kochi and Ernakulam, yet it is also separated by water. As a result, this location has been chosen for future study.
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2. SITE ANALYSIS
Site area Source - google.co.in/maps(Author)
The site is approximately 2,50,000 square metres in size and is located on the outskirts of Willingdon Island. According to Kerala development regulations, the site under consideration falls within the residential category.
Development plan Source - townplanning.kerala.gov.in
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Site context Source - google.co.in/maps(Author)
The site is surrounded on two sides by the dense population of Kochi and Ernakulam, yet it is secluded by the water of Vembanad Lake and accessible to the city by two highways. The property features two trails that lead from the water’s edge.
Pathways Source - google.co.in/maps(Author)
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Site Images Source - Author
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3. DESIGN INTENT
Intent of design Source - Author
The various forms and patterns that exist in nature have specific spiritual significance and these forms can help to uplift human consciousness and balance the physical, emotional, social and spiritual aspects of life, which gives us a higher sense of purpose, peace and hope. It also enhances Self confidence and self control which changes perspective of life by increasing inner strength to understand the relation between yourself and the world as a whole . If the space is formed using these geometries, it will enhance the quality and experience of life through their energies and vibrations. Hence the purpose of this research is to design a Holistic healing centre by amalgamating energies and vibrations of sacred geometric patterns.
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4. DESIGN PROGRAMME
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LIST OF FIGURES CHAPTER 1
The visual representation of sacred
(Source - academia.edusoft.ro)
The way towards the sacred
(Source - blog.spiritualify.com)
Secular, spiritual and religious existential orientations
(Source - www.sciencedirect.com)
Science and Spirituality as two sides of the same sacred coin
(Source - wallup.net)
Connection between spirituality and consciousness
(Source - www.dreamstime.com)
Detoriation of soul and body
(Source - www.dreamstime.com)
Strength of Sacredness
(Source - www.dreamstime.com)
Understanding sacred space
(Source - www.archdaily.com)
Sacred Space Elements
(Source - pinterest.com)
Space and Volume quality
(Source - archinatureindetail.wordpress.com)
Scale of human to the structure
(Source - www.archdaily.com)
Proportion of structure to context
(Source - www.archdaily.com)
Proportion of structure to context
(Source - www.archdaily.com)
Quality of Light in the Structure
(Source - www.archdaily.com)
Form of Sacred Structure
(Source - www.archdaily.com)
Sacred Structure
(Source - trendhunter.com)
Importance of Geometry in a Sacred Space
(Source - trendhunter.com)
CHAPTER 2
Sacred geometric forms create blueprints for design
(Source - Sacred Geometry by Jemma Foster)
Geometry of Universe
(Source - shutterstock.com)
Sacred Geometry and Chakras
(Source - pixels.com)
Scientific Geometry (Source - sciencedirect.com) Origin of Geometry
(Source - emaze.com)
Geometry and Nature
(Source - medium.com)
Geometry of Nature
(Source - newearthknowledge.com)
Geometry in Architecture, Math and Art
(Source - bleckarchitects.com)
Geometry of circle
(Source - 123rf.com)
Geometry of solar eclipse
(Source - nationalgeographic.com)
Geometry of Moon
(Source - joy-pup.com)
Sacredness of circle
(Source - en.wikipedia.org)
Arrangment of Stone Henge
(Source - cen.acs.org)
Geometry of Sphere
(Source - geometrycode.com)
Geometry of Dandelion Flower
(Source - pixabay.com)
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Geometry of Planet (Source - scientias.nl)
Geometry of Bubble
(Source - needpix.com)
Geometry of water droplets (Source - pixabay.com)
Geometry of Triangle
(Source - pixabay.com)
Sacredness of triangle (Source - pixabay.com)
Geometry of triangle in architecture (Source - pixabay.com)
Energy of Triangle
(Source - pixabay.com)
Fractal Forms development (Source - medium.com)
Fractal Energies
(Source - shutterstock.com)
Infinite fractal perimeter (Source - quora.com)
Fractals in tree branches (Source - theconsciousvibe.com)
Fractal in rivers
(Source - theconsciousvibe.com)
Fractal in mountains
(Source - theconsciousvibe.com)
Fractal in Plants
(Source - theconsciousvibe.com)
Fractal in Human DNA
(Source - theconsciousvibe.com)
Fractal in Universe
(Source - theconsciousvibe.com)
Vesica piscis
(Source - boanerges.edu.pl)
Vesica piscis and spirituality
(Source - tattoodaze.com)
Evolution of vesics piscis (Source - flickr.com)
Vesica piscis in Nature
(Source - quotesgram.com)
Vesica piscis and spirituaity (Source - quotesgram.com)
Geometry of Spiral
(Source - iconspng.com)
Spiral in Architecture
(Source - agefotostock.com)
Spiral in ancient art
(Source - zhirayravetisyan.com)
Spiral in solar system (Source - steemit.com)
Geometry of Merkaba (Source - shutterstock.com)
Energies of Merkaba
(Source - behealthywithana.com)
Concept of Merkaba
(Source - thebluebudha.com)
Geometry of Metatron’s cube
(Source - shutterstock.com)
Metatron’s cube in nature (Source - wdrfree.com)
Metatron’s cube and Platonic Solids
(Source - sagegoddess.com)
Flower of Life
(Source - shutterstock.com)
Elements of Flower of life (Source - imgur.com)
Seed of Life in Christianity
(Source - tumblr.com)
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Tree of Life in Judaism (Source - dreamstime.com)
Evolution of Flower of Life (Source - crystalinks.com)
Evolution of Flower of Life (Source - crystalinks.com)
Sacredness of Flower of Life (Source - onetribeapparel.com)
CHAPTER 3
Platonic Solids
(Source - daviddarling.info)
Plato
(Source - aenetworks.com)
Platonic Solids and 5 elements on the earth
(Source - whitman.edu)
Kepler
(Source - researchgate.net)
Platonic solids in Sphere
(Source - en.wikipedia.org)
Kepler Solar System
(Source - math.ucr.edu)
Tetrahedron
(Source - en.wikipedia.org)
Tetrahedron and Fire
(Source - sacredgeometryshop.com)
Tetrahedron and atomic molecule
(Source - sacredgeometryshop.com)
Tetrahedron in Merkaba
(Source - thebluebudha.com)
Hexahedron
(Source - en.wikipedia.org)
Hexahedron and Earth
(Source - sacredgeometryshop.com)
Hexahedron and Atomic Molecules (Source - sacredgeometryshop.com)
Tetrahedron in nature (Source - hr.bebee.com)
Octahedron
(Source - en.wikipedia.org)
Octahedron and Air
(Source - sacredgeometryshop.com)
Octahedron in nature
(Source - sacredgeometryshop.com)
Octahedron and Atomic Molecules (Source - sacredgeometryshop.com)
Dodecahedron
(Source - en.wikipedia.org)
Dodecahedron and Ether (Source - sacredgeometryshop.com)
Dodecahedron and Atomic Molecules (Source - sacredgeometryshop.com)
Dodecahedron in nature
(Source - sacredgeometryshop.com)
Platonic Solids in space (Source - sign.com)
Platonic Solids and Spirituality (Source - hu.pinterest.com)
Golden Section
(Source - elegantthemes.com)
Vitruvius man and golden ratio (Source - crl.nitech.ac.jp)
Golden Ratio in Plants
(Source - en.wikipedia.org)
Golden ratio in Universe
(Source - kiwihellenist.com)
Golden ratio in Animals
(Source - quickanddirtytips.com)
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Golden ratio and Mathematics (Source - medium.com)
Golden ratio and Geometric Calculations (Source - goldennumber.net)
Application of Fibonacci Sequence (Source - dreamstime.com)
Fibonacci Sequence in nature (Source - quora.com)
Leonardo Fibonacci (Source - thoughtco.com)
Fibonacci method
(Source - r-knott.surrey.ac.uk)
Fibonacci Sequence in nature (Source - pixels.com)
Fibonacci Sequence calculation
(Source - r-knott.surrey.ac.uk)
Fibonacci Sequence and geometry
(Source - researchgate.net)
Fibonacci Sequence in 3rd dimension (Source - semanticscholar.org)
Fibonacci Sequence and Sacred mathematics (Source - newearthknowledge.com)
Phi and sacred geometry (Source - youtube.com)
Calculation of Phi
(Source - interestingengineering.com)
CHAPTER 4
Phi and sacred geometry
(Source - youtube.com)
Calculation of golden ratio(step 1)
(Source - sacredgeometryshop.com)
Calculation of golden ratio(step 2) (Source - sacredgeometryshop.com)
Formula of golden ratio
(Source - en.wikipedia.org)
CHAPTER 5
Occurence of Sacred Geometry in Different Time Periods
(Source - Author)
View of Giza Pyramids
(Source - www.prints-online.com)
Earth-moon Pyramid and Pi relationship (Source - elementalorgone.co.uk)
Encoding Phi- 1: 1.618
(Source - scontent.fbom)
Planning with Golden ratio
(Source - alchemisoul.tumblr.com)
Incorporation of golden ratio in elevation
(Source - plus.maths.org)
Proportions of structure with golden ratio (Source - mathematicsmagazine.com)
View of Notre Dame Cathedral
(Source - pickyourtrail.com)
Tree of Life incorporating in plan
(Source - sciencedirect.com)
Plan and Relation with human body (Source - sciencedirect.com)
Golden Ratio in elevation
(Source - notre-dame-de-paris.net)
Openings and Vesica Picsis
(Source - notre-dame-de-paris.net)
The angles of the pyramid and squaring the circle (Source - sciencedirect.com)
3D Rendering of the project (Source - sciencedirect.com)
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3D Rendering of the project (Source - cnu.org)
City planning (step 1) (Source - cnu.org)
City planning (step 2) (Source - cnu.org)
City planning (step 3) (Source - cnu.org)
City planning (step 4) (Source - cnu.org)
City planning (step 5) (Source - cnu.org)
View of Washington City (Source -thoughtco.com)
City planning (step 6) (Source - cnu.org)
Plans incorporating golden rectangle (Source - degruyter.com)
Plans incorporating golden rectangle (Source - degruyter.com)
Incorporation of golden ratio in section (Source - degruyter.com)
Incorporation of golden ratio in section (Source - degruyter.com)
Sanchi Stupa and the use of Sacred Geometry (Source - ritiriwaz.com, in.pinterest.com, Edit - Author)
Gupta Dynasty
(Source - silentpagesindia.blogspot.com)
Chandella Dynasty
(Source - tripoto.com)
Monumental Temple (Source - freepressjournal.in)
Vijaynagara Dynasty
(Source - gosahin.com)
View of the Temple (Source - d-lab.kr)
Elevations of the Kandariya Mahadev Temple (Source - d-lab.kr)
Fractal Planning (Image Source - d-lab.kr, Edit - Author)
Box Method Calculations (Source - d-lab.kr)
Planning on the basis of Golden Rectangles (Source - d-lab.kr)
Analysing Kandariya Temple Geometry wiht Box method (Source - d-lab.kr)
Proportion of Shikharas (Source - d-lab.kr)
Carvings of natural objects (Source - d-lab.kr)
CHAPTER 6
Spiral of Galaxy (Source - space.com)
Dual Helix in DNA
(Source - businessinsider.in)
Platonic Solids
(Source - sacredgeometryshop.com)
Basic Forms in Nature (Source - joy-pup.com)
Relation of Sacred forms and souls (Source - fractalenlightenment.com)
Energies of Atomic Particles (Source - eandt.theiet.org)
Energies of a Triangle
(Source - slunecnabrana.eu)
Aura of Metratron’s Cube (Source - evolutionaryascension.com)
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DECIPHERING THE SACRED
Spiral connecting soul to universe (Source - shambali.com)
Energies of Merkaba
(Source - dreamstime.com)
Changing form with changing frequencies
(Source - pinterest.com)
Seven Chakras and Sacred Geometry (Source - musicenergetics.net)
Meditation and Sacredness (Source - thriveglobal.com)
Vitruvius Man and Sacred Geometry (Source - sw-ke.facebook.com)
CHAPTER 6
Planning of Auroville (Source - auroville.org, twitter.com)
Planning of Matrimandir (Source - auroville.org)
Figures of Sacred Geometry in MatriMandir (Source - mind-matrix.net)
Matrimandir and Cosmology (Source - mind-matrix.net)
Floor Plan at the Inner Chamber (Source - mind-matrix.net)
Internal Spaces of the Matrimandir (Source - mind-matrix.net)
Site Plan of Quiet Healing Centre
(Source - pdfcoffee.com)
3D Rendering of the project (Source - Nasa India NG Trophy 2012 LSRSA)
Project Plan
(Source - Nasa India NG Trophy 2012 LSRSA)
Sectional Elevation (Source - Nasa India NG Trophy 2012 LSRSA)
View of the buttress
(Source - Nasa India NG Trophy 2012 LSRSA)
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BIBLIOGRAPHY 1, L. E. (2021, June 27). Sacred geometry explained and how it can improve our daily life. Thrive Global. Retrieved March 21, 2022, from https://thriveglobal.com/stories/sacredgeometry-explained-and-how-it-can-improve-our-daily-life/ Ajmera, A. (2020, June 27). Role of geometry on architecture. International Journal of Engineering Research & Technology. Retrieved March 21, 2022, from https://www.ijert. org/role-of-geometry-on-architecture Dhwty. (2020, July 11). Sacred geometry: Unlocking the secret structures of the universe. Ancient Origins. Retrieved March 21, 2022, from https://www.ancient-origins.net/historyfamous-people/sacred-geometry-0013969 Geometry in nature: The fibonacci sequence. Villa di Maria Montessori School Blog. (2017, August 27). Retrieved March 21, 2022, from http://www.montessori-blog.org/2017/08/29/ geometry-in-nature-the-fibonacci-sequence/ How geometry has shaped the World Around Us. StudyPug. (n.d.). Retrieved March 21, 2022, from https://www.studypug.com/blog/how-geometry-has-shaped-the-world-around-us/ Hui, G. (2021, July 8). Sacred geometry: Creating sacred space. INCENTRE. Retrieved March 21, 2022, from https://www.incentrelondon.com/blog/sacred-geometry-creating-sacredspace Introduction. The Geometry Code. (2017, November 26). Retrieved March 21, 2022, from https://www.geometrycode.com/sacred-geometry/ Matthews, C. L. (2015, December 14). The seed of life and the Vesica Piscis. Metaphysical Corner. Retrieved March 21, 2022, from https://blog.etemetaphysical.com/seedoflife/ Mbuthia, M. (2020, April 11). What you should know about sacred geometry shapes. Legit.ng - Nigeria news. Retrieved March 21, 2022, from https://www.legit.ng/1317309-15-commonsacred-geometry-symbols-meanings-explained.html Museum, C. D. (2020, March 31). Finding geometry in nature. Medium. Retrieved March 21, 2022, from https://medium.com/purple-museum/finding-geometry-in-nature Sarah Regan , Spirituality & Relationships Writer. (2021, April 20). The spiritual meaning of shapes: A glimpse into sacred geometry + how to use it. mindbodygreen. Retrieved March 21, 2022, from https://www.mindbodygreen.com/articles/sacred-geometry Bodycherish. (n.d.). Sacred Geometry & the Triangle. BODYCHERISH. Retrieved March 21, 2022, from https://bodycherish.ca/blogs/holistic-health/40918017-sacred-geometrythe-triangle “Journey, T. E., & Jafet, A. (2021, November 19). Sacred Geometry Symbols & Meanings (amazing!). The. Retrieved March 21, 2022, from https://theenlightenmentjourney. com/2021/01/sacred-geometry-symbols-meanings.html#9_The_Dodecahedron”
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Davidson, S., 22, S. D. on J., & *, N. (2018, June 3). Sacred circles: No beginning and no end. sharmon davidson art. Retrieved March 21, 2022, from https://sharmondavidson.com/ sacred-circles/ Davis, B. (2021, April 30). Home. MVOrganizing. Retrieved March 21, 2022, from https:// www.mvorganizing.org/what-is-the-importance-of-patterns/ Encyclopædia Britannica, inc. (n.d.). Sacred. Encyclopædia Britannica. Retrieved March 21, 2022, from https://www.britannica.com/topic/sacred Gems In Style. (n.d.). Triangle – the power of your consciousness. Gems In Style. Retrieved March 21, 2022, from https://gemsinstyle.com/blogs/news/triangle-the-power-of-yourconsciousness Gern, M. (2018, June 26). What does the phrase “ Sacred science “ suggest to you. Academia. edu. Retrieved March 21, 2022, from https://www.academia.edu/36922607/WHAT_DOES_ THE_PHRASE_SACRED_SCIENCE_SUGGEST_TO_YOU Shermer, M. (2008, July 1). Sacred science: Using faith to explain anomalies in physics. Scientific American. Retrieved March 21, 2022, from https://www.scientificamerican. com/article/sacred-science/ Srivastava, D. P. (2017, March 10). Importance of spirituality in the contemporary world - New Delhi Times - India only international newspaper. New Delhi Times. Retrieved March 21, 2022, from https://www.newdelhitimes.com/importance-of-spirituality-in-thecontemporary-world123/ Tana, M. (1970, January 1). Sacred geometry: Triangle. mandalland. Retrieved March 21, 2022, from http://mandalland.blogspot.com/2009/03/sacred-geometry-triangle.html Denis. (2021, November 15). 10 importance of spirituality in daily life, education and health. Mind Controversy. Retrieved March 21, 2022, from https://www.mindcontroversy.com/ importance-of-spirituality/ Barrallo, J., González-Quintial, F., & Sánchez-Beitia, S. (2015, May 30). An introduction to the Vesica Piscis, the Reuleaux triangle and related geometric constructions in Modern Architecture - Nexus Network Journal. SpringerLink. Retrieved March 21, 2022, from https://link.springer.com/article/10.1007/s00004-015-0253-9 Beyer, C. (2018, May 4). What do spirals symbolize in religion and spirituality? Learn Religions. Retrieved March 21, 2022, from https://www.learnreligions.com/spirals-95990 Chris. (2020, June 21). Sacred geometry: The seed of life, Vesica Piscis, and the Merkaba. Enter The Earth. Retrieved March 21, 2022, from https://www.entertheearth.com/ seedoflife/ Destination Deluxe. (2021, December 18). Sacred geometry explained - what is the meaning behind the patterns? Destination Deluxe. Retrieved March 21, 2022, from https:// destinationdeluxe.com/sacred-geometry-explained-healing-benefits/
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Jay, N. (2020, July 27). Vesica Piscis (Pisces) – symbolic meaning and origins. Symbol Sage. Retrieved March 21, 2022, from https://symbolsage.com/vesica-piscis-pisces-symbolicmeaning/ Karakas, F., & Sarigollu, E. (2017, June 30). Spirals of spirituality: A qualitative study exploring dynamic patterns of spirituality in Turkish organizations - journal of business ethics. SpringerLink. Retrieved March 21, 2022, from https://link.springer.com/ article/10.1007/s10551-017-3619-y Payg, E. G. N., Fiolet, S., Martinez, H., Gil, Luciew, M., Field, E., Wills, T., Amormino, J., park100, Ledr, C, J., Beth, Trapanese, R., Leonora, Kamna, G., Jesse, & Zayas, S. (2021, July 6). A lot of knowledge in two circles: The Vesica Piscis - Sacred Geometry. Sacred Creation. Retrieved March 21, 2022, from https://www.sacredgeometryshop.com/sacred-geometry/vesicapiscis-sacred-geometry/ Thomas, B., Ladd, L., Roe, V., & Kizela. (2018, July 28). Vesica Piscis. Spiritus Lumine. Retrieved March 21, 2022, from https://spirituslumine.com/vesica-piscis/ Davis, F. (2021, June 4). Merkaba Sacred Geometry: How to activate your star tetrahedron light body. Cosmic Cuts. Retrieved March 21, 2022, from https://cosmiccuts.com/blogs/ healing-stones-blog/merkaba-sacred-geometry Hopler, W. (2019, May 23). What is Archangel Metatron’s cube in sacred geometry? Learn Religions. Retrieved March 21, 2022, from https://www.learnreligions.com/archangelmetatrons-cube-in-sacred-geometry-124293 Jay, N. (2022, February 5). What is a Metatron’s cube - and why is it significant? Symbol Sage. Retrieved March 21, 2022, from https://symbolsage.com/metatron-cube-symbolism/ Swift, B. (2018, December 14). Sacred geometry 101: An introduction to metatron’s cube. PHIDLE Sacred Geometry Clothing. Retrieved March 21, 2022, from https://www.phidle. com/blogs/sacred-geometry/sacred-geometry-101-an-introduction-to-metatrons-cube Dunno, S. (2020, April 15). What is the Flower of Life? Culture Cross. Retrieved March 21, 2022, from https://www.culture-cross.org/blogs/news/what-is-the-flower-of-life G. Z. M. G., Braun, A., Devi, U., Huhman, B. (2019, August 15). Unveiling the mystics of sacred geometry ~ fractal enlightenment. Fractal Enlightenment. Retrieved March 21, 2022, from https://fractalenlightenment.com/12086/artwork/unveiling-the-mystics-of-sacredgeometry Davis, F., & Davis, F. (n.d.). The spiritual meaning of sacred geometry shapes & platonic solids. Cosmic Cuts. Retrieved March 21, 2022, from https://cosmiccuts.com/blogs/ healing-stones-blog/sacred-geometry-shapes Dubois, L., Jones, L., love, M., Fiolet, S., & Ingleby, T. (2021, November 3). The spiritual meaning of the Platonic solids. Sacred Creation. Retrieved March 21, 2022, from https:// www.sacredgeometryshop.com/spirituality/the-spiritual-meaning-platonic-solids/
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Journey, T. E., & Jafet, A. (2021, November 19). Sacred Geometry Symbols & Meanings (amazing!). The. Retrieved March 21, 2022, from https://theenlightenmentjourney. com/2021/01/sacred-geometry-symbols-meanings.html#9_The_Dodecahedron Matt, Fiolet, S., Sargasree, M., & James, M. (2021, July 6). Platonic solids as building blocks. Sacred Creation. Retrieved March 21, 2022, from https://www.sacredgeometryshop.com/ sacred-geometry/platonic-solids-as-building-blocks/ Rayne, V. (2018, October 22). Sacred geometry. Discover Your Spiritual Gifts. Retrieved March 21, 2022, from https://discoveryourspiritualgifts.com/dysg-blog/364-sacredgeometry Vedantu. (2021, May 3). Platonic solid. VEDANTU. Retrieved March 21, 2022, from https:// www.vedantu.com/maths/platonic-solid Academysacredgeometry.com. About Sacred Geometry. (n.d.). Retrieved April 21, 2022, from https://www.academysacredgeometry.com/about-sacred-geometry Admin. (2021, July 16). Indus Architecture: The Architecture of Indus Civilization that is mainly observable in Moenjodaro and Harappa had three basic characteristics. Story Of Pakistan. Retrieved April 21, 2022, from https://storyofpakistan.com/indus-architecture/ Andrewhoskins, Susan, Uday, Marketing, F., Andrewhoskins, Lonny, Rosita, Site, M., Tina, Naomi, Doreen, Fullwood, A., Gilpin, C., Tinyurl.com, & Bit.ly. (2019, June 14). Pyramids and sacred geometry. Elemental Orgone. Retrieved April 21, 2022, from https://elementalorgone. co.uk/pyramids-sacred-geometry/ Architecture design and sacred geometry principles - ibiza Spain. IBIZALIVING Natural Lifestyle Architects Firm in IBIZA Spain. (2019, December 19). Retrieved April 21, 2022, from https://www.ibizaliving.net/about/sacred-geometry/ The Buddhist Stupa: Architecture & Symbolism • Approach Guides. Approach Guides. (2021, May 2). Retrieved April 21, 2022, from https://www.approachguides.com/blog/ buddhist-stupa-architecture-symbolism/ Davis, F. (2021, June 4). Merkaba Sacred Geometry: How to activate your star tetrahedron light body. Cosmic Cuts. Retrieved April 21, 2022, from https://cosmiccuts.com/blogs/ healing-stones-blog/merkaba-sacred-geometry Davis, F., & Davis, F. (n.d.). The spiritual meaning of sacred geometry shapes & platonic solids. Cosmic Cuts. Retrieved April 21, 2022, from https://cosmiccuts.com/blogs/ healing-stones-blog/sacred-geometry-shapes Destination Deluxe. (2022, April 21). Sacred geometry explained - what is the meaning behind the patterns? Destination Deluxe. Retrieved April 21, 2022, from https:// destinationdeluxe.com/sacred-geometry-explained-healing-benefits/ Golden Math. Sacred Geometry. (2012, August 6). Retrieved April 21, 2022, from https:// www.sacred-geometry.es/?q=en%2Fcontent%2Fgolden-math
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Gillan, J. (2020, August 19). The golden ratio – a sacred number linking the past to the present. Ancient Origins. Retrieved April 21, 2022, from https://www.ancient-origins.net/ unexplained-phenomena/golden-ratio-sacred-number-links-past-present-001091 Hopler, W. (2019, May 23). What is Archangel Metatron’s cube in sacred geometry? Learn Religions. Retrieved April 21, 2022, from https://www.learnreligions.com/archangelmetatrons-cube-in-sacred-geometry-124293 The importance of observing patterns in everyday life – a primer on sacred geometry. Stephens & Stevens - Marital & Family Law. (2021, January 16). Retrieved April 21, 2022, from https://eddiestephens.com/sacred-geo/ Magazine, S. (2008, April 30). A brief history of Pierre L’Enfant and Washington, D.C. Smithsonian.com. Retrieved April 21, 2022, from https://www.smithsonianmag.com/ arts-culture/a-brief-history-of-pierre-lenfant-and-washington-dc-39487784/ Matt, Fiolet, S., Sargasree, M., & James, M. (2021, July 6). Platonic solids as building blocks. Sacred Creation. Retrieved April 21, 2022, from https://www.sacredgeometryshop.com/ sacred-geometry/platonic-solids-as-building-blocks/ Meisner, G., Anonymvs, Ananya, Ella, Chaz, Trey, Tan, V., Pell, J., Anonymous, Meisner, G. B., Shaun, Nemo, Mukta, & bright, E. (2020, October 12). The Parthenon and phi, the golden ratio. The Golden Ratio: Phi, 1.618. Retrieved April 21, 2022, from https://www.goldennumber. net/parthenon-phi-golden-ratio/ The perfection of geometry. Official Website of Sadhguru, Isha Foundation. (2021, November 14). Retrieved April 21, 2022, from https://isha.sadhguru.org/in/en/wisdom/ sadhguru-spot/perfection-of-geometry Phi. Sacred Geometry. (2020, July 7). Retrieved April 21, 2022, from https://www. sacredgeometry.blog/phi/ Ramzy, N. S. (2021, February 27). Concept cathedral and “Squaring the circle”: Interpreting the Gothic Cathedral of notre dame de paris as a standing hymn. Frontiers of Architectural Research. Retrieved April 21, 2022, from https://www.sciencedirect.com/science/article/ pii/S209526352100008X Rian, I. M., Park, J.-H., Ahn, H. U., & Chang, D. (2007, April 23). Fractal geometry as the synthesis of Hindu cosmology in Kandariya Mahadev Temple, khajuraho. Building and Environment. Retrieved April 21, 2022, from https://www.sciencedirect.com/science/ article/abs/pii/S0360132307000273 Spiritual meaning of numbers: Sacred numbers & numerology. Universe of Symbolism. (n.d.). Retrieved April 21, 2022, from https://www.universeofsymbolism.com/spiritualmeaning-of-numbers.html
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