Visualising and representing

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

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

Can you find the link between these beautiful circle patterns and Farey Sequences?

Use the diagram to investigate the classical Pythagorean means.

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

Explore the lattice and vector structure of this crystal.

Starting with two basic vector steps, which destinations can you reach on a vector walk?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?