Although the origin of the golden ratio is unknown the golden ratio has been a topic of fascination for over 2,400 years. The first known calculation of the golden ratio was written by Michael Maestlin in 1597, but it's existence and significance were known long before that. It's thought by a man named Mario Livio that lots of people, other then mathematicians, have a fascination with the golden ratio. People like artists, biologists, musicians, architects, etc. It's a widely known concept thats been around for longer than is possible to track.
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"A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser." A Description of the golden ratio by Euclid's Elements
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The greek letter Phi is used to represent the golden ratio. The golden ratio goes by many names including, "golden mean", "golden section", etc. The first 16 digits of phi are 1.618033988749895... and keep going from there, though phi is usually rounded to 1.618. The ratio is found by taking a line a dividing it into two sections A and B. The length of A divided by the length of B should be equal to the length of A plus B divided A. The golden ratio ends up being 1:1.618, 1 being B and 1.618 being A.
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In 1509 Luca Pacioli published a three volume book called De Divina Proportione. The book looks into the mathematics of the golden ratio, Pacioli thought the golden ratio was a pleasing ratio to the eye. Pacioli was a mathematician, yet he had a fascination for art. De Divina Proportione contains art illustrated by Leonardo da Vinci, Pacioli's friend and collaborator.
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The golden ratio can be found in many things from nature, to architecture, to even the human face. The theory of beauty in the golden ratio has been widely known and believed by many. The Parthenon's front face is a perfect golden ratio rectangle, and there are lots of other cases of the golden ratio in architecture. Some architectural designs were purposely created to fit the golden ratio and others are not.
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The golden ratio is found in nature as well. The Fibonacci number sequence fits into the golden ratio, and both are often found in nature. To the left are two pictures of leafy plants. Each plants rows of leaves fit the golden ratio spiral, and each plant has a fibonacci number amount of rows. (To clear up confusion look at the pictures on the left.) Lots of other leafy plants, flowers, trees, and even grown food from plants hold the golden ratio.
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The idea of human perfection is a topic that is debated about and many don’t agree that there is such thing. It is thought that the golden ratio could have something to do with some people being seen as more “beautiful” than other people.
To measure perfection in the human face you could use the golden ratio to make many measurements across the face. The ratio of a+b to a and a to b makes the shape of a rectangle inside a rectangle. This shape is used to measure things like the distance between your top lip, bottom lip, and where your lips meet. |