Bowls
 © Islington Artefact Library
These three bowls demonstrate different types of pattern: radial, spiralling, repeating and symmetric. The study of patterns is at the heart of mathematics. Patterns occur in things such as numbers, shapes, spaces, positions and graphs, as well as in nature and everyday objects.

Patterns can be made by taking one shape or design and rotating it, repeating it or reflecting it repeatedly. These types of operations are known as slides, flips and turns. Patterns occur in numbers as well, and are called sequences. Pascal, a French mathematician, created a number pattern known as Pascal's triangle. A 1 is placed at the top of the triangle. Then two 1s are placed on the row below. Subsequent rows are made by inserting the number of 1s that is the sum of the two numbers that appear in the two rows directly above it, to form a triangle.

If a set of shapes can fit together snugly without leaving any gaps, they are said to tessellate. Some shapes (for example a hexagon) tessellate by themselves, without the need for any additional shapes. Others need an additional shape to fill gaps and make a larger tessellating shape. Have a look at the surface of a football.