Golden Ratio

Related to the Fibonacci sequence.

Also expressed as the Greek letter phi (φ), this irrational number pops up when the ratio of two numbers is the same as the ratio of their sum to the largest of the two numbers. It has been observed in many fields of the natural sciences at every scale and is has become associated with aesthetic beauty, giving it a nearly mythic reputation for some.

Expressed algebraicly:

Expressed as line segments:

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Golden Ratio

Related to the golden ratio and phyllotaxis.

Radial version of the golden ratio. It is the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio; that is, into two arcs such that the ratio of the length of the smaller arc to the length of the larger arc is the same as the ratio of the length of the larger arc to the full circumference of the circle.

In degrees the angle is approximately 137.5077640500 ..., or just 137.5 for brevity.

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