The golden ratio is a number that exists in anatomy, art, and the sciences. The estimated number is 1.61803399. To find the ratio, you find:
(1 + squaroot(5))/2
The numbers for the golden ratio are 1.618
It is considered that a shape, eg. Rectangle, with the golden ratio looks "most pleasing to the eye".
The Golden ratio = [1 + sqrt(5)]/2
The pentagram is related to the golden ratio, because the diagonals of a pentagram sections each other in the golden ratio. The Fibonacci numbers are also related to the golden ratio. Take two following Fibonacci numbers and divide them. So you have 2:1, 3:2, 5:3, 8:5 and so on. This sequence is going to the golden ratio
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A ratio is the quotient of two numbers. The golden ratio is the number 1/2 of [ 1 + sqrt(5) ] . A single number doesn't have a ratio.
The value of the Golden Ratio is (1 + sqrt(5))/2. It is visually appealing because it is!
Because it is an unusual ratio and therefore should be given a different name to differentiate it from other common ratios. Gold is valuable and "Golden" is attributed to that which is attractive. The "Golden Ration" is considered attractive and has many uses.
The golden ratio (golden section) is the division of a line so that the whole is to the greater part as that part is to the smaller part (i.e., in a ratio of 1 to 1/2 (√5 + 1)), a proportion that is considered to be particularly pleasing to the eye.
(1+sqrt(5))/2 This ratio is related to Fibonnacci numbers if you want to know more about it
The golden ratio is not a ratio of two whole numbers but an irrational number. It is 0.5*(1+sqrt(5)). Because it is irrational you cannot find two whole numbers such that their ratio equals the golden ratio. All you can do is get closer and closer to it. 62/38 = 1.6315789 618/382 = 1.6178010 and so on.
There are both golden triangles and golden rectangles. In order to be considered golden the ratio must be the same as the sum of the longest side to the other two sides.