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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