# 4

= 2 × 2
A square.

1, 3, 4, 7, 11, 18, 29...
A Lucas number.

A quartet, a foursome...

The word four has four letters. In the English language there is no other number whose number of letters is equal to its value.

The number four on a calculator is made up of four light bars.

Many things are arranged in fours. There are four suits in a deck of cards, four points of the compass, and four phases of the moon. There are four wings on a bee and four leaves on a clover, if you are lucky.

The four seasons are spring, summer, autumn and winter. This theme has provided inspiration for many artists, for the composer Vivaldi, and for countless take-away pizza establishments.

A tetrahedron is a kind of pyramid with four triangular faces. It also has four corners.

On maps adjacent countries are usually shown in different colours. What is the smallest number of colours needed? In 1852 Francis Guthrie guessed that the answer is four colours for any map, no matter what shape the countries take.

No one has ever found a map that needs more than four colours. But it has been difficult to find a satisfactory proof that only four colours are needed. In 1976 Wolfgang Haken and Kenneth Appel claimed to have proved the four-colour conjecture, but their proof is so complicated, involving hundreds of hours of calculation by a computer, it has been very difficult for other mathematicians to check.

Draw an imaginary map where the countries have very complicated shapes. Then try to colour them in with no more than four colours, and with no adjoining countries sharing the same colour. You may have to try colouring in several ways before you find a solution that requires only four colours.

A tetrahedron and a milk carton roughly in the shape of a tetrahedron.

Tetra- means four. A tetradite is someone who attaches mystical properties to the number four. A tetragram is a word with four letters (like four itself).

Quad- also means four. A quadruped is a four-footed animal like an aardvark, or almost any animal for that matter.

Plus fours are loose baggy trousers which require an extra four inches of cloth in tailoring. This ridiculous male fashion was popular with golfers in the 1920s.

In a molecule of DNA, just four bases are used to make up the genetic code that determines the distinctive form of every plant and animal. The four bases are called thymine, adenosine, guanine and cytosine, or just T, A, G and C.

Four-dimensional means that something has an extra dimension as well as length, width and depth. For the scientist, this is usually the dimension of time, where space and time are thought of as part of the same continuum.

However, in mathematics, four-dimensional means an imaginary fourth dimension in space. With two dimensions you can draw a square and with three dimensions you can make a cube. But with four dimensions it is possible to represent something called a hypercube. Some mathematicians claim to be able to visualise four-dimensional space and can conjure up a clear picture in their heads of a hypercube, which they can rotate or cut in half.