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Symmetric Trace

Points off a rolling wheel make traces. What makes those traces have symmetry?

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Mapping the Wandering Circle

In the diagram the point P can move to different places around the dotted circle. Each position P takes will fix a corresponding position for P'. As P moves around on that circle what will P' do?

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Like a Circle in a Spiral

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

The Line and Its Strange Pair

Age 14 to 16 Challenge Level:

Choose positions for P' and plot the corresponding positions of P.

Do enough until you see something nice happening then figure out why that has to happen.