### 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 ?

### 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?

### 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:
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.