it is exactly (1 + √5)/2 which is approximately 1.618034
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The value of the Golden Ratio is (1 + sqrt(5))/2. It is visually appealing because it is!
As you expand the Fibonacci series, each new value in proportion to the previous approaches the Golden Ratio.
The golden ratio is the ideal ratio because it is consistent throughout many aspects in nature - proportions of the human body, the crests and troughs of a heartbeat, the stripes on a tiger's head, et cetera. The value of the Golden Ratio is 0.5*[1 + sqrt(5)] = 1.61803 (to 5 dp)
A golden rectangle is a rectangle whose side lengths are in the golden ratio, approximately 1:1.618. Some whole number pairs of side lengths that approximate a golden rectangle include 1:2, 2:3, 3:5, 5:8, and so on. These pairs get closer to the golden ratio as the numbers increase.
The golden ratio is a pure number and so has no dimensions.The golden ratio is a pure number and so has no dimensions.The golden ratio is a pure number and so has no dimensions.The golden ratio is a pure number and so has no dimensions.