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?

Center Path

Four rods of equal length are hinged at their endpoints to form a rhombus. The diagonals meet at X. One edge is fixed, the opposite edge is allowed to move in the plane. Describe the locus of the point X and prove your assertion.

Rolling Coins

A blue coin rolls round two yellow coins which touch. The coins are the same size. How many revolutions does the blue coin make when it rolls all the way round the yellow coins? Investigate for a line of 'n' coins

Just Rolling Round

Stage: 4 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.