ACKNOWLEDGEMENTS
It’s a pleasure to be able to express my sincere thanks and gratitude for the advice, cooperation and support received from a large number of individuals that lead to the completion of this report. I am highly indebted to my guide, Ar. Vathsala Shrinivas for her guidance and constant supervision as well as for providing necessary information regarding the project and also for their unconditional support in completing the project. I am thankful to and fortunate enough to get constant encouragement, support and guidance from all the Teaching and non Teaching staff of the Department of Interior Designing, L.A.D. and Smt. R.P. College for Women, which helped me in successfully completing my project work. I would also like to express immense gratitude towards my friends and family for their kind co-operation and encouragement which helped me in completion of this project.
Sacred Geometry in Art and Architecture Aim of the Project: To uncover and establish correlations through analysis and interpretation of the architectural and design aspects with those of Sacred Geometry. Objectives of the Project: To study and analyze the use of Sacred Geometry in architecture and art from ancient civilizations and various architectural styles of the world To study the application of the principles of Sacred Geometry in religious architecture, design and art, with special reference to Islamic Architecture. To apply the principles of Sacred Geometry to the architecture and design of a contemporary mosque. Research Design and Method: This project discusses the formal and symbolical meaning of Sacred Geometry to architecture, design and classical art right from the Egyptian civilization to the present day religious structures, particularly those affiliated to the religion of Islam. The research presentation uses a mix of exploratory and descriptive research design mainly through the secondary research methodology. An interpretative and analytical approach has been adopted to discover new aspects that emerge from the study of architecture and design of traditional and religious structures from the rubric of Sacred Geometry. An effort has been made to study the architectural and interior elements a particular mosque in the city of Nagpur, using the Participant Observer method, to inspect the actual use of the principles of Sacred Geometry is an Islamic religious structure. The critical analysis in the case study concludes with design suggestions if the structure were to be made fully compliant with the principles of Sacred Geometry.
Sacred Geometry in Art and Architecture What is Sacred Geometry? Sacred geometry is the Geometry of consciousness that involves patterns used in the design of everything in our reality, it has most often been seen in ancient architecture and art. Apart from architecture twelve other informational systems, their geometry and proportions can be derived from sacred geometry. From Musical harmonics, light systems and cosmology to the periodic table and particle physics. This system of proportions has been found in all regions and time periods of the world and human history BODY
The sphere is considered a container that can hold all forms. It represents oneness, inclusion and integrity as all measurements are equal in a sphere. Planets, seeds, cells and atoms are all spheres.
MIND
After three spheres we get the holy trinity. A large number of informational systems can be derived from this shape. It is considered very sacred in most religions of the world
SPIRIT
The vesica pieces is a type of lens, a mathematical shape formed by the intersection of two disks with the same radius, intersecting in such a way that the center of each disk lies on the perimeter of the other.
It includes vast and incredible amount of knowledge about proportion, depth and roots of 2,3,& 5. It also is the basic form from with geometric information about light and music can be derived
FLOWER OF LIFE
4 circles
5 circles Creates exactly half of the pattern
The 'Seed of Life' is formed from seven circles being placed with six fold symmetry, forming a pattern of circles and lenses, which acts as a basic component of the Flower of Life's design. According to some, the seed of life depicts the 7 days of creation in which God created life
6 circles
Derivatives of ‘The Flower Of Life’ THE FRUIT OF LIFE
THE EGG OF LIFE
The 'Egg of Life' is also a symbol composed of seven circles taken from the design of the Flower of Life. The shape of the Egg of Life is said to be the shape of a multi-cellular embryo in its first hours of creation
The 'Fruit of Life' symbol is composed of 13 circles taken from the design of the Flower of Life. It is said to be the blueprint of the universe, containing the basis for the design of every atom, molecular structure, life form, and everything in existence. It contains the geometric basis for the delineation of Metatron's Cube, which brings forth the platonic solids.
If the centres of the spheres in the “Egg of Life’ are joined using straight lines. They create a perfect cube.
Metatron's cube
Star Tetrahedron (Star of David)
Hexahedron (cube)
Octahedron
Dodecahedron
Isosahedron
Metetron’s cube depicts the five platonic solids which may be derived form the flower of life. The five platonic solids are geometrical forms which are said to act as a template from which all life springs, according to spiritual belief. The Platonic solids are five structures that are crucial because they are the building blocks of organic life. These five structures are found in minerals, animated and organic life forms, sound, music, language, etc. Metatron's cube is also considered a holy glyph, used to ward off evil spirits. The Kabbalah's Tree of life is also thought to be derived from the flower of life.
Phi and Fibonacci principle
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship.
Phi and Fibonacci can be found everywhere in nature from plants to the human body.
THE FIBONACCI SPIRAL
Phi and Fibonacci principle derived from the Vesica pieces
Sacred Geometry in Reality Thirteen information systems can be derive from the flower of life pattern which include: LIGHT , its waves and geometry including it’s particle nature can be derived from the flower of life. The flower of life is evidently visible everywhere in NATURE
MUSICAL HARMONICS, and their fractions and ratios can be derived from a tetrahedron
The proportions of the HUMAN BODY follow the Phi and Fibonacci principle
The governing principles of ARCHITECTURE, geometry and proportion are derived from the Phi ratio
The basic process of genesis and creation follows the flower of life principle
Every pattern formed by the particles on a molecule follow the flower of life pattern and geometry
The elements in the PERIODIC TABLE with their atomic masses can be derived from the geometry of the flower of life
Sacred Geometry in Art and Architecture ARCHITECTURE
ART
EGYPTIAN SCULPTURE EGYPTIAN
GREEK
GREEK
SCULPTURE
INDIAN ROMAN
WINDOWS GOTHIC
(ROSE)
RENAISSANCE JAPANESE
NATIVE AMARICAN
BAROQUE
MANDALAS
INDIAN
ISLAMIC
ISLAMIC
Sacred Geometry in Architecture GREECE
Height of the columns – The structural beam on top of the columns is in a golden ratio proportion to the height of the columns. Note that each of the grid lines is a golden ratio proportion of the one below it, so the third golden ratio grid line from the bottom to the top at the base of the support beam represents a length that is 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 in golden ratio proportion to the height of the support beam. Width of the columns – The width of the columns is in a golden ratio proportion formed by the distance from the center line of the columns to the outside of the columns.
The orders were always constructed in proportion to the diameter of the base of the column. The diameter was then divided into 60 parts, each part called a minute. All the details, carvings and projections of the entablature and column= were measured in minutes
Sacred geometry in Architecture PARIS
The Eiffel tower in Paris also follows the golden ratio, From the entire height of the tower to the smaller divisions it is based on Phi and the golden rectangle and hence it doesn’t look out of proportion and has such a great aesthetic value
Notre Dame in Paris, which was built in between 1163 and 1250 appears to have golden ratio proportions in a number of its key proportions of design. Although it is rather asymmetrical in its design and difficult to measure photographically because of parallax distortions, the golden ratio lines of the green, blue and red rectangles conform closely to the major architectural lines, which represent: Red – Vertical height of base at ground level : Top of first level : Top of second floor Blue – Vertical height of base of second level : Top of second level : Top of third level Green – Horizontal width of outside of left top section : Inside of top right section : Outside of top right section:
Sacred geometry in Architecture MILAN
ROME PANTHEON The dome and its symbolism is what’s important. The dome maps a relationship of earth and man to heaven. This is why they went to such great effort to make a solid concrete ceiling. The floor tiles give an overall layout for how this done- a circle inside a square. The circle represents the celestial and the square the earthly. The form of the Pantheon is derived from the circle and square in plan and section view. This is the most basic application of the Flower Of Life.
St. PETER’S BASILICA
Bramante’s buildings in Milan show Vitruvian influence, especially in plan. The use of sacred geometry is not pure; instead composites of circles and squares overlap to form the church plans. The spatial conglomeration of the composite creates its own effect, but it is surely not the same as it would be if it were pure sacred geometry.
Bramante and Julius II began to design the reconstruction of St. Peter’s Basilica in sacred symmetry. The square plan considers how processions had become an integral part of Catholic worship at the time, the form of the Basilica divides into quadrants separated by four processional naves to form a Greek Cross in plan. The central meeting point of the naves forms a circle, where a dome would have enclosed and elevated the space. This plan is as egalitarian as it is sacred, yet the processional requirement of the church, like in the Basilica being replaced, demanded more focus on the Pope-led ceremony. With the addition of an axial nave to the design long after Bramante’s death in the end of the 16th century, the reconstruction of St. Peter’s Basilica exists today as yet another composite.
Sacred geometry in Architecture EGYPT
The construction of the Great Pyramid is based on proportions Phi = 1.618. The architects of the pyramids embodied in the stones the founding principles of the sacred geometry: The perimeter of the base of the Great Pyramid divided by the double height gives pi -3.1415 … (921.45 / 2 * 146.6 = 3.142). The perimeter of the base is equal to the length of the circle whose radius is equal to the height of the pyramid (2 * 3.14159 * 146.6 = 921). The length of the fundamentals expressed in the Egyptian „cubits“ (one of the values is 0.635 m) corresponds to the length of Earth’s year (230 / 0.63 = 365). The sum of the four sides of the pyramid – 921.45 m, is equal to half a minute of the width of the equator. One degree of the width of the equator covers 110,573 meters, and each arc minute – 1842.88 meters, which is more than twice the perimeter of the pyramid. If you multiply the original height of the Great Pyramid – 146.6 m by 1 million you get the smallest distance from the Earth to the Sun – about 147,098,074 kilometers (perihelion). The ratio of the original height of the Great Pyramid to its base was 7:11. This ratio has a number of important geometric properties. It contains the numbers Pi and Phi. The size of each of the borderlines of the pyramid is equal to the square of its height. The length of the borders of the pyramid divided by height gives Phi – 1,618. The length in feet – 484.4 corresponds to 5813 inches (5-8-13 – numbers of the Fibonacci sequence).
Sacred geometry in Architecture INDIA
JAPAN
The Golden Ratio and Fibonaci Sequence was well-known to Veda Vyasa and the Sages as an essential mathematical ratio synonymous with the “form of beauty” of divine nature. eg: it says the height of the temple should be double its width, and the height of the foundation above the ground with the steps equal to a third of this height. The sanctum sanctorum should be half the width of the temple and so on. These guidelines translate into various interpretations of the Golden mean
Plans of temples constructed according to the flower of life
The Yakushi-ji Temple built in Nara, in about 680 AD is one of the seven great Buddhist temples in Japan. the Hosso Sect of Japanese Buddhism and was dedicated to the Medicine Buddha. Originally two great pagodas stood at the east entry to the temple complex. Like all stupas, the pagoda was an architectural embodiment of the Buddha which sits on the first floor with its crown at the topmost roof. The structure is based on a square plan symbolizing the body. The pagoda appears to have six stories due to the intermediate pent roofs, but there are actually three which represent the 3 main divisions of the Universe in Buddhist Cosmology: The World of Desire, The World of Form and the Formless Worlds. A wooden mast sits in the center, the spine of the Buddha connecting heaven and earth Above the highest roof this extends having 9 rings, the number of steps to enlightenment in the higher planes. Above this the sacred Jewel representing Enlightenment. Overlaid on the Buddha is the star pentagram, the geometry of perfected being, which establishes the golden Ø proportions of the building and of the Buddhas 3 Bodies (Trikaya).
Sacred geometry in Art LEONARDO DA VINCI Da Vinci created the illustrations for the book “De Divina Proportione” (The Divine Proportion) by Luca Pacioli. It was written in about 1497 and first published in 1509. In the book, Pacioli writes of mathematical and artistic proportion, especially the mathematics of the golden ratio and its application in art and architecture. Some geometric solids, such as dodecahedrons and icosahedrons, have inherent golden ratios in their dimensions and spatial positions of their intersecting lines. Other examples of golden ratios in the illustrations include the one architectural illustration in the book and the one script letter (G) that is not divided horizontally at its midpoint.
Da Vinci’s use of the Divine proportion is evident in some of his own works, even before his collaboration with Pacioli. The paintings I reviewed suggest that the use of the Divine proportion in paintings among Renaissance artists may have been more common in paintings of special religious significance.
Golden ratios from left side to precise center of canvas, which aligns with the mountain peak. Note positioning of angle face and wings, as well as position of the one tree in the background that’s different from all the others.
The peaks of the mountains in relation to the top of the canvas are in golden ratio proportion
The ornamentation of the table is at the golden mean of its width
Perhaps one of the best illustrations of its use is in “The Last Supper,” painted between 1494 and 1498. Various design and architectural features show very clear golden ratios. Some believe that even the positions of the disciples around the table were placed in divine proportions to Jesus.
Sacred geometry in Art LEONARDO DA VINCI
Leonardo da Vinici, is well known for his usage of the Fibonacci Sequence. One notable example is his most famous work, The Mona Lisa. Da Vinci utilized the sequence with the Golden Spiral, which stems from the Perfect Rectangle. The Perfect Rectangle is formed by creating rectangles within the corresponding dimensions of 1.618, from each descending Fibonacci Number (8, 5, 3, 2, 1, etc.) The spiral comes from touching each side in the Perfect Rectangle. The Golden Spiral can best be seen in the shell of a Nautilus.
The Vitruvian Man illustrates a variety of different proportions in the human body. With arms outstretched, a man is as wide as he is tall, with the genitals as the midpoint. (Green) The knees are halfway between the genitals and the feet. (Blue) The chest is halfway between the genitals and the top of the head. (Blue) The chest is the same width as a quarter of the height. (Red) The measurement from the elbow to the fingertips is also a quarter of the height (Red) The nose is halfway between the hairline and the chin. (Orange) The eyebrows are halfway between the nose and hairline. (Orange) The lips are halfway between the nose and chin. (Orange) The head is one-eighth the total height. The hand is one-tenth the total height. The foot is one-sixth the total height.
Sacred geometry in Art MIICHELANGELO Michelangelo repeated this theme of the characters touching the golden ratio point in other paintings of the Sistine Chapel, as illustrated in the four paintings below. The green lines show the golden ratio of the height and/or width of each painting.
The point at which the fingers of God and Adam touch in “The Creation of Adam by Michelangelo. This is found at the golden ratio of both their horizontal and vertical dimensions. Click on the image for full resolution: The same golden ratio point appears if you instead use the inside or outside borders of the painting, rather than the borders of God and Adam.
Each of the paintings on the center section of the ceiling is framed by two larger ceiling sections that separate the paintings. For seven of the nine paintings, the width of the painting is a golden ratio of a golden ratio. This simply means that you take the golden ratio of a dimension (red grid) and then in turn take the golden ratio of that dimension (blue grid), as illustrated below:
Sacred geometry in Art RAPHAEL The golden rectangle that was placed front and center in the painting. It’s as though Raphael made a small but undeniable statement to answer the question before it was asked. This small rectangle is about 18″ by 11.1″ and is a rather unusual feature. Perhaps it once bore the title or some description of the painting. Even the framed area immediately below it shows a framed that is in golden ratio proportion to the borders on its sides.
The painting has thousands of intricate lines, the golden ratios are very evident on the major elements of the composition. Note that simple golden ratios of the width and height of the painting define the positions of the large wall of the first arch, the top of stairs at the floor and the top of the second arch.
To appreciate the intricacy and depth of Raphael’s planning and application of the dimensional proportions in this painting, consider the illustration below. This image includes four rectangles that overlay the painting: Each rectangle begins at the left side of the left column in the painting. This point represents the first architectural reference point of the actual school building as viewed through the arched portal of the fresco. Each extends to a prominent composition feature on the right side of the painting. Each is divided into one or more golden ratios. Each dividing line illustrates a golden ratio formed within another prominent feature of the composition. Trace the four rectangles separately, each in its own color, following it until you see the golden ratios that are revealed. It may be easiest to look first at the rectangles as overlayed onto a black background,
Sacred geometry in Art INDIAN ART
The Golden Ratio and Fibonaci Sequence was well-known to Veda Vyasa and the Sages as an essential mathematical ratio synonymous with the “form of beauty” of divine nature, here exemplified in Sri Krishna.
Vastu Sastra is an ancient Indian science of architecture and proportions that employs the Golden Ratio extensively for designing and building energetically and aesthetically optimal temples, chariots and dwellings — as well as deities which are worshiped in temples all over the world, but especially in India.
Sacred Stone from Gandaki river in Himalays called, “Saligram Sila” worshiped for millennia as a “natural manifestation of Lord Vishnu.”
This image of Lord Vishnu shows an intricate use of the Golden Ratio
The swastika symbol is prominent in Hinduism, which is considered the parent religion of Buddhism and Jainism, both dating from about the sixth century BC, and both borrowing the swastika from their parent. Buddhism in particular enjoyed great success, spreading eastward and taking hold in southeast Asia, China, Korea and Japan by the end of the first millennium. The use of the swastika by the indigenous Bon faith of Tibet, as well as syncretic religions, such as Cao Dai of Vietnam and Falun Gong of China, is thought to be borrowed from Buddhism as well. Similarly, the existence of the swastika as a solar symbol among the Akan civilization of southwest Africa may have been the result of cultural transfer along the African slave routes around 1500 AD. The right-facing swastika may be described as "clockwise"...... or "counter-clockwise"A swastika composed of 17 squares in a 5x5 grid. Geometrically, the swastika can be regarded as an irregular icosagon or 20-sided polygon. The arms are of varying width and are often rectilinear (but need not be). Only in modern use are the exact proportions considered important: for example, the proportions of the Nazi swastika were based on a 5x5 grid. The swastika is chiral, with no reflectional symmetry, but both mirrorimage forms have 90° rotational symmetry (that is, the symmetry of the cyclic group C4).
Sacred geometry in Art EGYPTIAN ART The Egyptians had a deep understanding of the golden ratio and the flower of life and hence it can be seen in their art, architecture and sculpture. From the Great pyramids and temples to the paintings on the walls and sculptures of the pharos, the proportions and geometry are sacred and seemingly perfect. Representations of the human figure in ancient Egyptian art usually conformed to highly stylized principles in which the proportions between the different parts of the human body were determined by a set of fixed laws constituting a Canon of Proportions. Egyptian artists were thereby able to make use of a conventional system of proportion which was found to be aesthetically pleasing, while also rendering their subjects in idealized forms which may or may not have been faithful to the exact proportions of the persons in question.
Sacred geometry in Art GREEK SCULPTURE
In some Greek sculptures the navel (belly button) represents the mean of the golden ratio: The nevel is positioned such that the ratio of the short half to the long half is equal to the ratio of the long half to the whole. From feet to navel= 1 From feet to head= 1,618 Ancient sculptors used canons—sets of “perfect” mathematical ratios and proportions—to depict the human form. The earliest known canons were developed by the Egyptians, whose grid-based proportions influenced Greek sculptors in the Archaic period (700–480 B.C.). Over time, sculptors and painters sought to create a canon that would allow them to depict the perfect human body—not a body based on a real person but a body based on a defined harmony among parts. This idea prevailed into the Classical and Hellenistic periods even as artists became increasingly interested in presenting the human body in more natural poses
Sacred geometry in Art MANDALAS
The word Mandala derives from the Hindu language meaning 'concentric energy circle.' A circle represents protection, good luck, or completion. Mandalas link with the spiralling movement of consciousness, sacred geometry, psychology, and healing. It is a spiritual and ritual symbol in Hinduism and Buddhism, representing the Universe. The basic form of most mandalas is a square with four gates containing a circle with a center point. Each gate is in the general shape of a T. Mandalas often exhibit radial balance. In various spiritual traditions, mandalas may be employed for focusing attention of aspirants and adepts, as a spiritual teaching tool, for establishing a sacred space, and as an aid to meditation and trance induction.
The basic design of the mandala is found in most cultures as all of reality follows the same creational blueprint.
Sacred geometry in Islamic Art and Architecture
The craft guilds of Islam were crucial to upholding the knowledge that it is important to grasp that geometry is not simply a practical art for making things; it also has a deeper, more profound meaning – practically, philosophically, and, most importantly, cosmologically. Geometry should be regarded as an eternally sacred art form that not only puts the practitioner in touch with the ‘eternal’ and thereby nourishes, his or her soul, but also the potential to awaken the sacred in the souls of those who experience what the practitioner produces.
Any Islamic pattern is a challenge to the mind and to that part of our consciousness that wants to know how such pattern has come about. The laws of two- and three- geometry are inevitable and ‘woven’ into every pattern. Technical knowledge of the laws of the regular grids and regular solids becomes a spinal grid on which to understand how the Islamic genius has utilized the same knowledge.
Sacred geometry in Islamic Art and Architecture
According to the lore passed on through traditional craft guilds, the compass and square or straight edge, used respectively for making circles and straight lines, are symbolic of the heavenly realm and earthly domain. The mastery of these tools id traditionally equated with ‘true man’, practitioner of geometric arts/sciences and ‘mediator’ between heaven and earth. In the passing on of the practice of traditional geometry, great importance is placed on both, the demonstration of skill of drawing in front of the student and on the study of good examples of traditional art and craft and their relationship to a particular environmental context.
Islamic patterns are expressed as woven. This weaving effect has a double – or more – symbolic meaning. It touches on the personal path where an individual ‘way’ meets that of another and a decision has to be made, either to be ‘submissive’ [go under] or ‘ assertive’ 9go above], which roles alternate.
Sacred geometry in Islamic Art and Architecture Basic shapes fundamental to Islamic geometric patterns CIRCLE
EQUILATERAL TRIANGLE
The circle, representing the active point of the compass returning to its own point of departure, is a good symbol of timeless whole, while the moving point itself represents the passing of time as it describes the circle.
The development from point to line to plane by overlapping and tangenting circles. The radius becomes the edge length of the equilateral triangle and the module for the primary grid of triangles The division of a circle into multiples of six has a powerful influence on th human experience of time as well as its significance relating to the circle as a symbol of ‘perfection’. The ancient Sumerians gave the world a sexagesimal (base 60) numeral earth’s cycle around the sun: 60 seconds in a minute and 60 minutes in an hour and 60x6=360, the approximate number of days in a year. Also the circumference of the circle divides perfectly into six parts by its own radius. This provides the essential diagram for constructing a number of key Islamic patterns.
Triangle is the most stable figure it of the world. The equilateral triangle is one of the three all-space-filling polygons (the other two being the square and hexagon). The equilateral triangle divided equally from its apex to ts base reveals a highly significant triangle containing the root three proportional system. Plato, identifies this figure as one of the two most beautiful triangles underlying the structure of the universe , the other being the triangle made by halving the square which contains the root two proportional syatem
Sacred geometry in Islamic Art and Architecture SQUARE
HEXAGON
Six is regarded as the number of perfection and symbol of heaven, perhaps because its qualities are co closely tied to the circle. The number holds a unique position in mathematics because it is the only number that is both the sum and product of its parts: 1+2+3= 1x2x3= 6. The development of a square from the circle ( flower of life)
The square is one of the three shapes that make the repeated geometric patterns known as primary grids, or tessellations, using a single shape.
The six-ness of the hexagon has also been spoken of as relating to the six periods of creation. To the classical, six hundred was in addition the number symbolizing the cosmos.
Traditionally the square is associated with the earth and four fold relationships found in the essential order of the natural environment. These include four cardinal directions (north south east and west), the four seasons (spring, summer, autumn and winter) , the four elements (earth, air, fire and water) and their qualities (hot, dry, moist and cold). In a geometric diagram of the four petal construction – a diagram par excellence for the construction of Islamic art and craft designs – another square, drawn from the middle of the sides of the first square where the lines of the second square cross each of the petals, also locates the corners of an octagon
A regular hexagon formed from the lower of life pattern The model of six overlapping circles around a central seventh circle can also be used to construct both the six-sided hexagon and 12-sided dodecagon. Both of these polygons can be combined with squares and equilateral triangles the make the underlying sub-grids for producing a variety of Islamic patterns
Sacred geometry in Islamic Art and Architecture
4 FOLD The basis of all geometric patterns in the Islamic culture start with a circle. The first major decision is how you divide the circle. Most patterns split the circle into four, five or six equal sections and each one gives rise to distinctive patterns. These patterns or this method of dividing the circle gives us the mother grid of all the patterns in existence
4 FOLD
5 FOLD
6 FOLD
Most of these patterns are stars surrounded by petal shapes. Counting the number of petals tells us what category the pattern falls into. A star with 6 rays or petals belongs in the 6 fold category, one with 8 petals is part of the 4 fold category and so on.
6 FOLD
This gives rise to fourfold, fivefold and six fold symmetry. These simple geometric forms are used to create incredibly complex geometric patters by the Islamic crafts men and are used everywhere in art and architecture
There is another ingredient, an underlying grid. Its invisible but essential to every pattern. The grid help determine the scale of the composition before work begins, keeps the pattern accurate and facilitates the invention of incredible new patterns
Sacred geometry in Islamic Art and Architecture Example showing the process of making Islamic geometric patterns 4 FOLD PATTERNS
Cell Pattern after Tessellation Every pattern starts with a circle within a square, and the circle is divided into eight equal parts.
Then a pair of crisscrossing lines is drawn, and overlaid with another two. These lines are called construction lines.
Cell Pattern after Tessellation
The next step is to choose a set of their segments. The only rule is that the segments should form a symmetrical pattern
This will form the basis of our repeating pattern. Many different designs are possible from the same construction lines, just by picking different segments
Cell Pattern after Tessellation
Sacred geometry in Islamic Art and Architecture The same steps can be followed by cutting a circle into six parts creating a six fold symmetric pattern
6 FOLD PATTERNS
Cell
Pattern after Tessellation
This patterns has appeared over the centuries and all over the Islamic world, it is one of the most widely used patterns by Islamic artists and designers.
MARRAKESH
AL-HAMBRAH
AGRA - INDIA Cell Pattern after Tessellation
Sacred geometry in Islamic Art and Architecture 5 FOLD PATTERNS
The resultant patterns may seem confoundingly complex but are still relatively simple to produce
Five fold patterns are more challenging to tessellate because pentagons do not neatly fill a surface. It is not a regular space-filling shape A lot of Islamic guilds and artists make use of this property of a pentagon to create astounding complex patterns that have a great appeal to the human eye.
In a pentagon, other shapes have to be added to make something that is repeatable.
In this example an irregular hexagon and a 10 sided polygon have been added and joined in such a manner that when repeated they fill the entire surface.
An example of a five fold geometric pattern
Sacred geometry in Islamic Art and Architecture
The weaving patterns in 4 fold, 5 fold and 6 fold symmetry
An example of six fold symmetric pattern used on the entrance of a masjid using mosaic tiles
A very complex 4 fold pattern
Step by step construction of a 4 fold pattern Step by step construction of a complex 5 fold pattern
Sacred geometry in Islamic Art and Architecture Islimi is one of the three disciplines that underpins Islamic art (the other two being calligraphy and geometry). The eternal spiral. Behind most designs, there is a spiral from which motifs and leaves sprout. The movement of nature inspires the unbroken flow of the spiral ; it has no hard corners, and the curves are sweeping and gentle. Symmetry Once a section of spirals is drawn, it is reflected and repeated to fill a page, wall or dome. Symmetry is fundamental to a harmonious design. Rhythm and balance These deigns tessellate across the surface with an even rhythm and texture Islimi is a key architectural feature, examples can be found in ornate ceramic, stone, plaster and wood carved friezes. Islimi designs are also found embellishing domestic objects such as utensils, cloths and carpets.
Motifs and styles / Origins and development Islimi designs gradually emerged as the floral, vegetative style of Islamic art in various forms around the world. As Islam spread and nations adopted the faith, they stylized their decorative arts to fit the principles of Islam. At the same time they were inspired by each other. Most notable influences were from Chinese and Byzantian arts.
Sacred geometry in Islamic Art and Architecture COMPOSITIONS
RUMI MOTIFS
Positioned at the heart of the Rumi motif is the ‘Pivotal ball’. Regardless of the shape the motif might take, it will always revolve around this ball. If a second motif is attached to the first it will also grow from this ball. The motif can be drawn geometrically which shows similarity to one half of the Taoist yin-yang symbol.
TEPELIK MOTIFS
Kapali means ‘closed’. Kapali forms are linear structural lines, which are usually based on an underlining geometric grid ensuring they reflect or tessellate correctly. The shapes are versatile and have architectural properties; the crown shape is used in domes and gateways across the Islamic world. Within a design it reflects itself and motifs helping patterns slot together.
An example of a subdividing design, displaying parallel Kapali and Spiral compositions
Gold kapali overlaying turquoise spirals; cut tiles from the Jameh ,osque in ifshan. Iran.
Tepelik means points or hilltops, it is the other major motif in the Rumi style. It is used both as a symmetrical freestanding motif and in half form attached the spiral.
Sacred geometry in Islamic Art and Architecture FLOORING
Construction of a hand-painted flooring tile in islimi
Construction of a flooring tile pattern (mosaic)
Construction of an inlaid marble floor border (islimi pettern)
Construction of a hardwood flooring pattern (4 fold)
Sacred geometry in Islamic Art and Architecture WALL CLADDING
Construction of a Wall tile pattern (mosaic) Construction of a Wall tile pattern (mosaic) in the corners of an archway
An islimi pattern used as inlay work in marble wall cladding.
Geometric as well as islimi used in plaster arabesque and mosaic tiles
An islimi pattern used in hand painted ‘haft-rangi’ tiles
Sacred geometry in Islamic Art and Architecture DOOR WAYS
WINDOW JALI
Sacred geometry in Islamic Art and Architecture Islamic rugs are heavy textiles made for a wide variety of utilitarian and symbolic purposes . The weaving of pile rugs is a time-consuming process which, depending on the quality and size of the rug, may take anywhere from a few months to several years to complete. To begin making a rug, one needs a foundation consisting of warps and wefts:. An oriental rug design uses a medallion or Mandala, a symmetrical pattern occupying the center of the field. Parts of the medallion, or similar, corresponding designs, are repeated at the four corners of the field.
Evolution of a geometric mandala pattern in the center of an islamic rug .
Examples of traditional islamic rugs.
Sacred geometry in Islamic Art and Architecture KARBANDI (RIBBED) VAULTING
TYPES OF KARBANDI VAULTS ‘Karbandi’ refers to the iconic roof structures in Iranian/Islamic classic architecture especially in bazars where the decoration and structure go hand in hand in the formation of the space. Dome is the most obvious reference of Iranian architecture having been present in every period and region. Karbandi is considered to be one of the advanced methods of this transition which moved ahead over time to find a proper construction as a symbol of thoughtful architecture. The unique geometrical capacities of karbandi made it possible to build dome in any context. The plan of the vault or dome is always a STAR and the rays of the star make the ribs of the dome. This is a classic example of sacred geometry being used in the structure of a building.
ELEVATON OF A TYPICAL KARBANDI VAULT
Sacred geometry in Islamic Art and Architecture 3D STRUCTURES FROM THE 2D ISLAMIC PATTERNS Muqarnas is the Arabic word for stalactite vault. It is an originally Islamic type of wall or ceiling decoration, which is used to make a smooth transition from the rectangular basis of the building to the vaulted ceiling. Muqarnas can also be seen in minarets, capitals of columns or eaves of a building.
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The earliest forms of muqarnas , found in the Mesopotamian region, were primarily structural.
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Muqarnas grew increasingly common and decorative in the beginning of the 12th century.
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Muqarnas ornament is significant in Islamic Architecture because it represents an ornamental form that conveys the vastness and complexity of Islamic ideology.
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It was believed that every atom composing a muqarnas dome was connected with God. The muqarnas domes were often constructed above portals of entry for the purpose of establishing a threshold between two worlds.
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When featured in the interior of domes, the viewer would look upward (towards heaven) and contemplate its beauty. Conversely, the downward hanging structures of the muqarnas represented God’s presence over the physical world.
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A Muqarna installation consists of tiers or layers which in turn consists of elements
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There is a great variety of these elements yet they can be more or less deduced from a small set of basic elements.
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Among these elements we can distinguish ‘cells’ and ‘intermediate’ elements.
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The cells look like small pieces of vault and they are the most important part of the muqarnas since they make up the body of the structure
Sacred geometry in Islamic Art and Architecture 3D STRUCTURES FROM THE 2D ISLAMIC PATTERNS
The most simple example of MUQARNA geometry is a column capital The process starts with a star plan. In this example, an 8 pointed star plan is used
All the tiers combined make half of the capital of a column. Half the plan is used to construct the Muqarnas. It is divides into 3 sections which make the three tiers of the capital.
The inner most star makes the bottom tier. Vertical elements are added to the base of the star Apak khoja mausoleum
Timur’s tomb, Samarqand
Palace of the lions, Spain
The second star makes the middle tier. Vertical elements are added to the star to make the facet and curve and hence making cells.
SOFIT OF ENTRANCES
The largest star makes the top tier. Vertical elements are again added to the star to make the cells.
ELEVATIONS
CORNERS OF BUILDINGS
INTERIOR OF DOMES
MINARETS
SQUINCHES
Sacred geometry in Islamic Art and Architecture 3D STRUCTURES FROM THE 2D ISLAMIC PATTERNS
Different styles of the shape of the curve gives different shapes to the cells adding to the aesthetic value Half dome/ half vault muqarna from a star plan
Construction the muqarnas in the dome of the mausoleum of Imam Dur
The plans of different types of muqarnas. They can range from very simple to very complex
Sacred geometry in Islamic Art and Architecture LAWS OF THE GOLDEN RATIO IN ISLAMC STRUCTURES Islamic architectural design and construction combines various secular and religious styles that span over all of the Islamic history. The bulk of Islamic architectural characteristics are visible in mosques, tombs, forts and palaces, but the evolution of Islamic architecture can be seen best in the construction of the mosques Islamic mathematicians like Al-Buzyani (998 AD.) and Giyath Al-Din Jamsid Al-Kashi (1429 AD.) had written a manual on the basic geometric principles and its applications in architecture. The manual contained issues on the 2D composite geometrical designs, fundamental lines of the dome and gateways, and these formed the characteristics of the muqarnas shaped-dome. This manual had also become the technical guidelines with mathematical principles for the architects, developers and building supervisors. Geometry plays a fundamental role in design of Islamic architectural monuments. From the viewpoint of exterior functioning, the use of geometry as art for creation of shapes, patterns and proportions reminds the Great Architecture of the World and recalls the Archetypes. From the viewpoint of interior functioning, geometry as science for selection of structural dimensions such as height, length and width of the building and its structural elements longer = φ shorter = 1 sum = φ 2 governs the structural behaviour of the building, the behaviour that follows the geometry. The right geometry makes the building behave correctly.
A typical mosque layout which includes the ‘Mihrab’ which is a niche and the most decorated part of the mosque, it faces the direction of Madina. Al-sultan Hassan Complex
Sacred geometry in Islamic Art and Architecture Specific units were used for the majority of the parts in a traditional building. An example of this is the usage of the specific brick size. This is done for the purpose of harmonizing various buildings put together. The measurement unit in Iran is called Gaz . All elements, especially openings used to be built based on this unit and its proportion.
ONE GEREH
1/16 GAZ
6.66 CM
ONE GAZ
16 GAREH
106.66 CM
In many buildings, the plan and elevation were set out in a framework of squares and equilateral triangles, whose intersections gave all the important fixed points, such as the width and height of doors, the width, length and height of galleries, the position of inscriptions, etc. For example, geometrical analysis shows that a complete knowledge of the Golden Ratio is applied in the plan of Persepolis (518-330 B.C.)
Two techniques are implemented so as to obtain the golden ratio in mosques which are the geometric construction and numerical analysis. The first technique involves the use of geometric approach by the partition of line and generation of the golden rectangle.
Plan of Persepolis, Shiraz, 518-330 B.C.
Elevation of Ali Qapu, Isfahan, 1597-1688 A.D.
Aesthetically, the Ali Qapu building (1597-1668 A.D.), in Isfahan, shows the application of the Golden Ratio in architecture. If the width of the building is considered as unity, important points such as the corners of the entrance to the building and the heights of different levels produce ratios of the Golden Ratio. The second technique is by the numerical analysis method, conducted in Excel. Initially, the structural measurements are calculated from the plan of the mosque. The analysis is carried out by dividing the greater to the lesser of the building given by the formula; Ratio = a/b≈1.61812297where a = the greater length and b = the lesser length.
The Minaret with 2nd Geometric Construction
. Ghasr-e-Khorshid (Reza zadeh Ardebili and Sabet Fard 2013).
Sacred geometry in Islamic Art and Architecture The Golden Ratio has been masterly used in the design of the Taj-al-Mulk dome dated 1088 A.D., in Jami mosque in Isfahan. Schroeder [5] thoroughly explains the aesthetic and geometrical features of the monument. He shows the sophisticated application of the Golden Ratio, in such a way that the lesser part is below, in the dimensions of the dome and the chamber below. His geometrical analysis proves that the architect of the building has taken a pentagon, which is generated between the sides of a grand equilateral triangle the apex of which is the peak of the dome,
The plan of the mosque of Coedoba shows the extent of the original 8th- century mosque (A) with the first 9th century extension (B). The diagram shows the courtyard = 1:1/2, and the original mosque = 1:1/2 which combine as a square. The first extension is calculated as part of the root2 rectangle.
The geometrical analysis of the plan is superimposed showing the use of an 8x8 square grid in conjunction with the root two system of diminishing squares, relating the central domed building of the fountain to the surrounding arcades (zidayas).
The Ibn tulun mosque, built in Cairo between 876 and 879, The geometric analysis of the perimeter of The plan of the great Umayyad mosque, built in damascuc between 709 and 715, is a golden mean rectangle. The construction of both, rectangle and equiangular spiral within it make some interesting correspondences with the internal divisions of the plan.
Sacred geometry in Islamic Art and Architecture In the plan of the Bu ‘Inaniyya Madrasa in Fez, Morocco , the courtyard and small mosque are surrounded by an irregular series of rooms, whereas the courtyard and mosque area make a rectangle of root 3 proportions
The golden ratio rules and Sacred geometry was also used in the construction and geometry of the arches. Namely the pointed arch. The pointed dome on minarets was also comstructed used according to the fin=bonacci and golden mean.
A geometric analysis shows the harmonious proportions behind the composition of the Taj mahal built in Agra, India, between 1632 and 1643. It is believed to be one of the building where the laws of sacred geometry have been found with clarity and are almost perfeect,
The root two system, derived from the diagonal to the side of a square
The root three proportional system
Sacred geometry in Islamic Art and Architecture BIBLIOGRAPHY Donato Bramante: Sacred Geometry in Rome 14 November 2013, Author : helenlevin • The Pantheon: Rome’s Architecture Of The Cosmos Benjamin Blankenbehler ,October 20, 2015 • The Parthenon and Phi, the Golden Ratio January 20, 2013 by Gary Meisner • Phi and the Golden Section in Architecture March 5, 2013 by Gary Meisner • Golden Ratio in Art and Architecture By Samuel Obara • Flower of Life Meaning, Origin, application, effect flower-of-life.net • http://www.crystalinks.com/vesicapiscis.html • https://www.invisibletemple.com/sacred-geometry-ofancient-temples.html • http://www.crystalinks.com/mandala.html • The Golden Ratio - Hidden Codes in Architecture • https://www.thoughtco.com/golden-ratio-hiddencodes-in-architecture-177599 • Scale and Proportion in Interior Design: The Golden Ratio By Mary Cook, 13.11.2015 • Sacred Geometry Introductory Tutorial by Bruce Rawles • http://aboutislam.net/science/faith-science/sacredgeometry-islamic-architecture/ • https://www.ancient-symbols.com/symbolsdirectory/tetractys.html • Golden Ratio Calculator By Piotr Małek and Mateusz Mucha • Michelangelo and the Art of the Golden Ratio in Design and Composition January 18, 2016 by Gary Meisner • Use of the Golden Rectangle in Interior Design https://homeguides.sfgate.com/use-golden-rectangle-i nterior-design-70020.html • List of works designed with the golden ratio • The designer's guide to the Golden Ratio By Creative Bloq Staff October 24, 2018 • Fractal geometry in nature and architecture By majalinse/ September 18, 2016 •
• The Sacral geometry of the Great Pyramid 18.03.2016 Marina Ivanova • The Cubit and the Egyptian Canon of Art John A.R. Legon • Muslim rule and compass: the magic of Islamic geometric design , By-Alex Bellos • Geometry – The Language of Symmetry in Islamic Art by Richard Henry • Heirloom Tech: The Math and Magic of Muqarnas By- Goli Mohommadi, Dec 16 2016 • http://wilhelmmeyer.transculturalstudies.ch/en/polychrom y/muqarnas.html • Bahri Mamluk muqarnas portals in Egypt: Survey and analysis, Author links open overlay panelMohamadKashef • http://islamicarchitecturebydxx.blogspot.com/2015/02/ba sic-definitions-muqarnas.html • https://www.slideshare.net/sharmiarchitect/muqarnasmathematics-in-islamic • Structural Genuine-Muqarnas Dome: Type Definition, Unit Analysis and Computer Generation System Mohammad-Ali Jalal Yaghan • https://www.slideshare.net/guneetkhurana1/geometry-ofislamic-architecture • https://www.nomadinception.com/islamic-design/islamicdesign-resources/islamic-architecture-islamicdecoration.html • Arts and crafts of the Islamic lands Edited by Khaled Azzam • Sacred geometry in nature and Persian architecture M. Hejazi Department of Civil Engineering, Faculty of Engineering, University of Isfahan, Iran • Is there any geometrical golden ratio in traditional iranian Courtyard houses? Faezeh nabavi, yahaya ahmad • Modelling Approach In Islamic Architectural Designs Suhaimi Salleh • ARCH241 | Modeling of Karbandi Dome 23 ARALIK 2018~ BEYZADEMİRR
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