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The title is a reference to the ancient Greek scuptor after whom the golden ratio was given the symbol phi(Φ).
x = √(1+√(1+√(1+√(1+...)))
x^2 = 1 + √(1+√(1+√(1+√(1+...)))
x^2 = 1 + x
x^2 - x - 1 = 0
The quadratic formula gives phi (1.61803...) as the larger solution.
x = 1+1/(1+1/(1+1/(1+1/(1+1/(1+...
x = 1+1/(x)
x^2 = x + 1
x^2 - x - 1 = 0
Which is the same equation as before. |
