How many different colours would be needed to colour these different patterns on a torus?

Some simple ideas about graph theory with a discussion of a proof of Euler's formula relating the numbers of vertces, edges and faces of a graph.

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .

This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.

Consider these weird universes and ways in which the stick man can shoot the robot in the back.

How can you represent the curvature of a cylinder on a flat piece of paper?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?

Can you make a new type of fair die with 14 faces by shaving the corners off a cube?

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

Put your visualisation skills to the test by seeing which of these molecules can be rotated onto each other.

This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.

The second in a series of articles on visualising and modelling shapes in the history of astronomy.