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.
You add 1 to the golden ratio to get its square. How do you find higher powers?