## Monday, April 28, 2014

### From Golden Ratio to golden arse

In mathematics, two quantities are in the golden ratio φ (phi, or 1.6180339887...) if their ratio is the same as the ratio of their sum to the larger of the two quantities.

Geometrically, the golden ratio represented as a line divided into two segments a and b, such that the entire line is to the longer a segment as the a segment is to the shorter b segment.

Expressed algebraically, for quantities a and b, with a > b

Many artists and architects have proportioned their works to approximate the golden ratio - especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio - believing this proportion to be aesthetically pleasing.

In geometry, a golden spiral is a logarithmic spiral whose growth factor is the golden ratio φ (phi). That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.

Here is the figure of an approximate and true Golden Spirals. The green spiral is made from quarter-circles tangent to the interior of each square, while the red spiral is a Golden Spiral. Overlapping portions appear in yellow. The length of the side of one square divided by that of the next smaller square is the golden ratio φ (phi).

Now, what do you get when you put 2 golden spirals together? ... A most aesthetically pleasing Golden Arse !

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