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Symmetric Trace

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

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The Line and Its Strange Pair

In the diagram the point P' can move to different places along the dotted line. Each position P' takes will fix a corresponding position for P. If P' moves along a straight line what does 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?

Mapping the Wandering Circle

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

You will certainly want to have looked at The Line and its Strange Pair to help you into this.