### 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.

### Tuning and Ratio

Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?

### Rarity

Show that it is rare for a ratio of ratios to be rational.

# Reductant Ratios

##### Age 16 to 18 Challenge Level:
The relative atomic masses of iron and oxygen are $56$ and $16$ respectively