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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?

A Scale for the Solar System

Age 14 to 16
Challenge Level

Draw the plan view. Imagine you are looking down on the plane containing the Sun, Earth and Venus. Put in circles to represent the orbits, none of the sizes will be right of course but the diagram can still be useful.

Choose a position for the Earth and then imagine Venus in all possible positions relative to Earth.

What's that view going to look like to an observer on Earth?