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Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, ...
You add two previous terms you get the next term.
If you put F(n) as the nth Fibonacci number,
the golden ratio (φ) is
lim(n→inf) F(n+1)/F(n)
that is because
F(n) = (φ^n-(-φ)^(-n))/(√5)
Other properties of φ
φ = (1+√(5))/2
1/φ = φ-1
φ2 = φ+1
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What is an experiment for the golden ratio of beauty?
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The ratio of dividing the larger Fibonacci number into the smaller Fibonacci number gives you the golden ratio (1.618 to 1). -------- The Golden Ratio is the number (1+sqrt(5))/2~=1.618 The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... . Skipping the first two terms, if you divide one term in this sequence by the previous term the resulting sequence converges to the Golden Ratio: 1.0000 2.0000 1.5000 1.6667 1.6000 1.6250 1.6154 1.6190 1.6176 1.6182 1.6180 Please see the link for more information.
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