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