Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.

Can you find the area of a parallelogram defined by two vectors?

Can you combine vectors to get from one point to another?

The article provides a summary of the elementary ideas about vectors usually met in school mathematics, describes what vectors are and how to add, subtract and multiply them by scalars and indicates. . . .

Can you work out the fraction of the original triangle that is covered by the inner triangle?

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

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?

Use vectors to collect as many gems as you can and bring them safely home!