# 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.