Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?

Explore the lattice and vector structure of this crystal.

Use the diagram to investigate the classical Pythagorean means.

Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?

Rajeev and Christian both explained their thinking about this probability problem very clearly.

In this article, we look at solids constructed using symmetries of their faces.

An article introducing continued fractions with some simple puzzles for the reader.

A java applet that takes you through the steps needed to solve a Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.