- Problem
- Getting Started
- Solution

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.

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 $b_n$.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.

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NRICH is part of the family of activities in the Millennium Mathematics Project.

NRICH is part of the family of activities in the Millennium Mathematics Project.