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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?

Contact

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?

Investigating the Dilution Series

Age 14 to 16
Challenge Level
It is not envisaged that this problem would be used as a class problem.  It is more appropriate for an enthusiastic student or small group of students looking for a challenge to work on independently.