problem

### Gold Yet Again

Nick Lord says "This problem encapsulates for me the best features
of the NRICH collection."

problem
###
Gold Yet Again

Nick Lord says "This problem encapsulates for me the best features
of the NRICH collection."

problem
###
Golden Fractions

Find the link between a sequence of continued fractions and the
ratio of succesive Fibonacci numbers.

problem
###
Golden Fibs

When is a Fibonacci sequence also a geometric sequence? When the
ratio of successive terms is the golden ratio!

problem
###
Pentakite

Given a regular pentagon, can you find the distance between two non-adjacent vertices?

problem
###
Golden Ratio

Solve an equation involving the Golden Ratio phi where the unknown
occurs as a power of phi.

problem
###
Pent

The diagram shows a regular pentagon with sides of unit length.
Find all the angles in the diagram. Prove that the quadrilateral
shown in red is a rhombus.

problem
###
Golden Powers

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

problem
###
Golden Triangle

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.

problem
###
Pythagorean Golden Means

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.