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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

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

Just Rolling Round

Age 14 to 16
Challenge Level

Experiment with the interactivity and make your own conjecture about the locus of $P$.

As the small circle moves, points on the small circle come into contact with points on the big circle. Think about the lengths of the arcs on the two circles that are made up of the points that have come into contact.