Visualising and representing

If you know some points on a line, can you work out other points in between?

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

Mark a point P inside a closed curve. Is it always possible to find two points that lie on the curve, such that P is the mid point of the line joining these two points?

Which curve is which, and how would you plan a route to pass between them?

Which line graph, equations and physical processes go together?

By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?

Explore the lattice and vector structure of this crystal.

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.