A circular plate has radius one unit. It rolls around inside a rectangular tray, always touching the edge, and returns to its starting position after five circuits of the tray. During this time it rotates about its own centre by seven complete revolutions.

The motion is said to be periodic because it repeats itself over and over again after each five circuits and the length of the period is 5 circuits.

Can you find the dimensions of the tray? Is there more than one solution?