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Age 16 to 18

Challenge Level

A length of thin wire ($L$ ) binds together two
cylindrical welding rods, whose radii are $R$ and $r$ , by passing all
the way around them both.
Find and
$r$.$R$ |

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

Imagine a rectangular tray lying flat on a table. Suppose that a plate lies on the tray and rolls around, in contact with the sides as it rolls. What can we say about the motion?