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Five Numbers

The Imaginary Number

If the square root of +1 is both +1 and -1, then what is the square root of -1?

• 14 mins

Five Numbers

Infinity

Georg Cantor defined infinity as the size of the never-ending list of counting numbers.

• 14 mins

Another Five Numbers

The Number Four

Are 4 colours enough to paint any map, so neighbouring countries have different colours?

• 14 mins

Another Five Numbers

The Number Seven

Are 7 shuffles sufficient to achieve a good degree of randomness in a deck of 52 cards?

• 14 mins

Another Five Numbers

The Largest Prime

Can large prime numbers be used to form the basis of more secure encryption codes?

• 14 mins

Another Five Numbers

Kepler's Conjecture

Is the 'face-centred cubic lattice' the most efficient way of stacking spheres?

• 14 mins

Another Five Numbers

Game Theory

When 3G phone licences were sold, game theory was used to boost proceeds for the Treasury.

• 14 mins

A Further Five Numbers

One - The most popular number

One is the most popular number, as it appears more often than any other number.

• 14 mins

A Further Five Numbers

Two - At the double

Doubling is a form of exponential growth, which appears in population growth and inflation

• 14 mins

A Further Five Numbers

Six degrees of separation

Six is often treated as 2x3, but has many characteristics of its own.

• 14 mins

A Further Five Numbers

G - The number that defines the universe

Newton's equation of gravity includes a number G, indicating the strength of gravitation.

• 14 mins

A Further Five Numbers

1729 - The first taxicab number

1729 is the smallest number you can write as the sum of two cubes, in two different ways.

• 14 mins