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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

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Locus problems that have elegant visual simplicity readily draw us into geometric reasoning because the pleasure of seeing what's going on is accessible.

This problem uses a mapping called Inversion Geometry which has wide application and works well as an aesthetically satisfying introduction to the concept of mapping.