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Phi is the Golden ratio.

It is a way of dividing a rectangle such that the ratio of the two sides of the whole rectangle are the same as the ratio of the sides of the smaller rectangle.

Using measurement units such that the small rectangle is 1*f, therefore the larger one is f*(f+1). f is actually phi, but this browser is not so good for Greek letters.

Equality of the ratios imply that 1/f = f/(f+1)

Cross-multiplying, f2 = f + 1

therefore f2 - f - 1 = 0

Using the quadratic formula, f = [1 + sqrt(1 + 4)]/2 - the other root is negative and so not appropriate for a length.

Therefore phi = f = [1 + sqrt(5)]/2 = 1.61803 (approx).

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