The Golden Spiral
The Golden Spiral was first discovered by Pythagoras in the 5th century B.C.
The spiral is derived from the golden rectangle, which has the ratio of 1.618:1. When the rectangle is cut into a square, it leaves a smaller rectangle behind, which has the same ratio as the previous rectangle. The squaring can continue indefinitely with the same result. A quarter of a circle is connected to each square forming the golden spiral.
This shape is found everywhere in nature: the Nautilus Shell, Ram's horns, the face of a Sunflower, fingerprints, DNA, and the shape of the Milky Way.
Choosing a photograph size that is closest to 1.618"1 will appear to be the most esthetic.
As demonstrated in the chapter "Aspect Ratios," the following sizes are closest to the "phi" ratio of 1.618:1 The phi ratio exists almost everywhere in nature.
Ratios of 1.5:1 are:
24 mm x 36 mm
4" x 6"
8" x 12"
12" x 18"
24" x 36"
Fibonacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
(add the two previous numbers to get the next number)
Fibonacci sequence becomes divisible by the phi ratio:
1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.666...
8/5 = 1.60
13/8 = 1.625
21/13 = 1.615...
34/21 = 1.619...
55/34 = 1.618...
89/55 = 1.618...
144/89 = 1.618...
Binary sequence:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024...
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