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. . . .

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

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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

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

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.

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

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.

A task which depends on members of the group working collaboratively to reach a single goal.

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

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

A task which depends on members of the group working collaboratively to reach a single goal.

How would you design the tiering of seats in a stadium so that all spectators have a good view?

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

Which faces are opposite each other when this net is folded into a cube?

Use trigonometry to determine whether solar eclipses on earth can be perfect.

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

The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.