The Golden Ratio is something that we see every day without even realising it. It’s found in art, architecture, music, the human body, design and nature to name just a few. But what exactly is the golden ratio and where does it come from? Matthew Cross, author and Golden ratio authority describes it as ‘nature’s perfect proportion for bringing parts together as a greater whole.’
The actual numerical value of the golden ratio is an irrational number, there is an infinite number of decimal places. However it is often simplified to 1:1.618. A golden rectangle is produced when using these values and interestingly this is thought to be the most visually pleasing shape. Adrian Benjan, a professor at Duke University says that ‘the human eye is capable of interpreting an image featuring the golden ratio faster than any other.’
“The Golden Ratio has inspired thinkers of all different disciplines like no other number in mathematics.” The Golden Ratio is something that has fascinated genius’ for years. It has influenced the work of Leonardo Da Vinci, Albert Einstein, Luca Pacioli amongst others. Astrophysicist Mario Livio says, ‘The Golden Ratio has inspired thinkers of all different disciplines like no other number in mathematics.’
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There are a huge amount of examples of the golden ratio in nature. Its found in seashells, pinecones, flowers, waves and even galaxy spirals. The way that that solar system fits together is thought to be based on the golden ratio and the fibonacci numbers. It is evident in numerous animals ranging from ants to dolphins, moths to penguins.
It is found in the anatomy of human beings over and over again. Our eyes, ears and facial structure. Our arms, hands and feet. Even the strands of our DNA work on a golden ratio framework. The sheer number of examples of the golden ratio in nature is astounding. It is clear that the golden ratio is a fundamental characteristic of the universe.
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“If the Golden Ratio makes the front of a building look fantastic, imagine what it can do for the backside of a woman.” -The Proportion of Blu
“When the ancients discovered ‘Phi’, they were certain they ha stumbled across God’s building block for the world.” -Dan Brow
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“the human eye is capable of interpreting an image featuring the golden ratio faster than any other.” -Adrian Bejan
“The golden ratio is arguably the most irrational of all irrational numbers,” -Mario Livio
“The golden ratio is the slowest of all continued fractions to converge,” -Mario Livio ‘The Golden Ratio has inspired thinkers of all different disciplines like no other number in mathematics’ -Marvo Livio
“Without mathem there is no art.” –Luca Pacioli
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“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
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“The Fibonacci Sequence turns out to be the key to understanding how nature designs... and is... a part of the same ubiquitous music of the spheres that builds harmony into atoms, molecules, crystals, shells, suns and galaxies and makes the Universe sing.” -Guy Murchie
“The description of this proportion as Golden or Divine is fitting perhaps because it is seen by many to open the door to a deeper understanding of beauty and spirituality in life.” - HE Huntley
“It is a scale of proportions which makes the bad difficult and the good easy.” -Albert Einstein
The Golden Ratio has been talked about for thousands of years. It is thought that the Ancient Egyptians were the first to recognise and understand it and that’s over 2000 years ago. Still the golden ratio continues to amaze great minds of today. On this page is a range of quotes on the subject.
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THE MATHS 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 left illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b
To the left is a figure of a line with two segments. The line segments are in the golden ratio with a as the longer segment and b as the shorter segment. When a line is split using the golden ratio a + b is to a as a is to b.
To the left is a figure showing a golden rectangle. If the longer side is a and the shorter side b, when placed adjacent to a square with sides of length a, another golden rectangle with longer side a+b and shorter side a will be produced
We see uses of the golden ratio in the work of artists, designers and photographers in the modern day. Despite being constantly surrounded by uses of the golden ratio we are often unaware of its presence
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It is thought that golden ratio proportions can be found in Egyptian, Sumerian and Greek vases, Chinese pottery, Olmec sculptures, and Cretan and Mycenaean products from the late Bronze Age. This is roughly 1,000 years before the Greek Mathmeticians first studied the ratio. Whether this was done on purpose or by chance, either way proves that the proportions are visually pleasing to the human eye.
We see artists, designers and photographers using these proportions to this day. Notably, designers at Apple have used the golden ratio and the fibonacci sequence within the design of many of their products and visuals. The logo is thought to have been created using these proportions along with companies such as Twitter Toyota, BP, Pepsi and numerous others.
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The golden ratio is known by many other names. One of which is Phi. This is the Greek word for this mysterious value, it was named after a famous Greek architect, Phidias. Phidias designed the Parthenon, a temple dedicated to Athena, an Ancient Greek Goddess. Although the temple is deteriorating golden ratio proportions are evident in the design of the building. The Ancient pyramids are another example of ancient architecture that is thought
to use golden ratio values in its design. This is the oldest example discovered. The ratio has been used in architecture throughout history though. We see it in the Notre Dame in Paris, (built in between 1163 and 1250) the Taj Mahal in Inida, (completed in 1648) and in modern day architecture. The UN building, the CN tower in Toronto and the values are thought to have been used in the design of the Empire State Building