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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.
1/2 [ 1 + sqrt(5) ]
The Fibonacci sequence can be used to determine the golden ratio. If you divide a term in the sequence by its predecessor, at suitably high values, it approaches the golden ratio.
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)