1/2 [ 1 + sqrt(5) ]
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The Golden Ratio is interesting due to it being in place throughout nature. The Golden Ratio is present within humans, several species of plants, and even in the shells of some species invertibrates.
MathYou can find the golden ratio in nature in some flowers such as the Cosmo, the iris, the buttercup, the daisy and the sunflower, it is also found in some fruits and vegetables such as the lemon, the apple, the chili and the artichoke.
No. The golden ratio appears in plants but not animals. Snail shells may grow in a spiraling (exponential) growth pattern but the golden ratio implies one particular growth rate which nature does not demand of them.
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)
No. The Golden ratio is an irrational number: [1 + sqrt(5)]/2 = 1.6180, approx. It is found in many patterns - in nature as well as man-made.