Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.
A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?
Four jewellers share their stock. Can you work out the relative values of their gems?
The area of a regular pentagon looks about twice as a big as the pentangle drawn within it.