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
Show that for any triangle it is always possible to construct 3
touching circles with centres at the vertices. Is it possible to
construct touching circles centred at the vertices of any polygon?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
This interactivity is designed for the problem Cushion
The interactive diagram below has two labelled points, A and B.
What is the shortest path from A to B if you bounce off one
cushion? In the diagram, you can click on the "Show" buttons to
draw the four possible paths from A to B. Which is the shortest?
You may move A and B around by clicking on them.
What is the shortest path from A to B using exactly two
cushions? The interactive diagram below shows the eight possible
paths from A to B. How would you calculate the shortest path?