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The golden ratio is a number, commonly known as phi (<math>\varphi</math>), defined as
The '''golden ratio''' is a number, commonly known as phi (<math>\varphi</math>), defined as
<math>\varphi^2 = \varphi + 1</math>. The value of phi is
<math>\varphi^2 = \varphi + 1</math>. The value of phi is
<blockquote>''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.''</blockquote>
<blockquote>''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.''</blockquote>
==The golden ratio in nature and art==
The golden ratio appears in innumerable places in nature and art. The [[golden ratio in the solar system|periods of the plants]] are all related by the golden ratio. The proportions of the bodies of many animals, including humans, dolphins, and ants are all based on the golden ratio. The [[Parthenon]], [[Egyptian Pyramids]], [[The Last Supper]], and even the common credit card are all based on the golden ratio.
A dodecahedron, a solid in which each side is a pentagon, is related to the Golden Ratio in that both the surface area and the volume of a dodecahedron of unit edge length are functions of the Golden Ratio. Plato described the dodecahedron as the solid ''which the gods used for embroidering the constellation on the whole heaven.''
A dodecahedron, a solid in which each side is a pentagon, is related to the Golden Ratio in that both the surface area and the volume of a dodecahedron of unit edge length are functions of the Golden Ratio. Plato described the dodecahedron as the solid ''which the gods used for embroidering the constellation on the whole heaven.''