What is the golden ratio The short answer is 1.61803398875 and.

The golden ratio was discovered by the Pythagoreans around 500 B.C.

The long answer will require some figures and some math.

Attach a 2-unit square( sum of the two previous side lengths) along a matching side length.

Attach a 3-unit square( sum of the two previous side lengths) along a matching side length.

Attach a 5-unit square( sum of the two previous side lengths) along a matching side length.

Finally, using the side length of each square as the radius, draw a quarter-circle arc in each square.All arcs should be connected.

If you do, the square should have the following side lengths: 8, 13, 21.

The lengths of all squares will give a Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21,.etc,.

If the quotient of each consecutive pair of numbers is formed ( for example, 11, 21, 32, 85, 138,.) the numbers produce a new sequence.

The first several terms of this new sequence are 1, 2, 1.5, 1.66., 1.6, 1.625, 1.61538,.

If we continue in this pattern, we will approach the decimal number 1.61803 This number can also be written as (1 5)2 and it is called the golden ratio.

At this point, what is the golden ratio if not a pain in the neck In a golden rectangle, we can identify two rectangles that are similar.

A big rectangle with sides a b and a and a small rectangle with sides b and a If we separate the small rectangle from the bigger and rotate the big rectangle 90 degrees counterclockwise.

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2021.09

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