article
Euler's formula
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.
Networks/graph theory
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articleTangles
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead? -
articleSymmetric tangles
The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why! -
articleThe four colour theorem
The Four Colour Conjecture was first stated just over 150 years ago, and finally proved conclusively in 1976. It is an outstanding example of how old ideas can be combined with new discoveries. prove a mathematical theorem. -
articleAn introduction to computer programming and mathematics
This article explains the concepts involved in scientific mathematical computing. It will be very useful and interesting to anyone interested in computer programming or mathematics. -
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articleA curious collection of bridges
Read about the problem that tickled Euler's curiosity and led to a new branch of mathematics!
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problemKnight defeated
Age14 to 16Challenge level
The knight's move on a chess board is 2 steps in one direction and one step in the other direction. Prove that a knight cannot visit every square on the board once and only (a tour) on a 2 by n board for any value of n. How many ways can a knight do this on a 3 by 4 board? -
problemW mates
Age16 to 18Challenge level
Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.