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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?


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

All about Ratios

Age 16 to 18 Challenge Level:
Can you work out the distances?

the problem