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The famous golden ratio is g={\sqrt5 + 1 \over 2}. Prove that g^2=g+1.
Let g^n = a_ng + b_n. Find the sequences of coefficients a_n and b_n.
Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.
Show that the arithmetic mean, geometric mean and harmonic mean of a and b can be the lengths of the sides of a right-angles triangle if and only if a = bx^3, where x is the Golden Ratio.
Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.