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Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

Roaming Rhombus

We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point D?

Triangles and Petals

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

Symmetric Trace

Age 14 to 16
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.