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Golden Thoughts

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.

At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?


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?

Half a Triangle

Age 14 to 16
Challenge Level
Triangle split 50-50 for area
Using only a pair of compasses, and an edge to draw a straight line along,
construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.