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?

Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

Just Opposite

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

Making Tracks

Stage: 4 Challenge Level:

Perhaps find a bicycle and experiment.

Or perhaps trace a curve on paper and imagine a cyclist following that curve with the front wheel, and then consider the possibilities for the back wheel ?

You may also like to consider the motions recorded in these three images. One line traces the path of a back wheel and one line traces the path of a front wheel: