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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.

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From All Corners

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

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Star Gazing

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

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?