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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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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?

Symmetric Trace

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
The main problem-solving tasks for the student here are :
  • To get a sense of how the wheel motion gives each trace.
  • To identify and accurately describe the geometric properties possessed by these traces.
  • And then to bring those two together in an account which connects what is observed in the trace with the characteristics of the motion.