ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

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?

This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.

From the information you are asked to work out where the picture was taken. Is there too much information? How accurate can your answer be?

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?

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 ?

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