** Mathematics** is the study of

Example of a four color map Image credit: |

The ** four color theorem** states that given any plane separated into regions, such as a political map of the counties of a state, the regions may be colored using no more than four

It is often the case that using only three colors is inadequate. This applies already to the map with one region surrounded by three other regions (even though with an even number of surrounding countries three colors are enough) and it is not at all difficult to prove that

The four color theorem was the first major

The lack of mathematical elegance was another factor, and to paraphrase comments of the time, "a good mathematical proof is like a poem — this is a telephone directory!"

A ** Lorenz curve** shows the distribution of

- ...that it is possible for a three dimensional figure to have a finite
volume but infinitesurface area ? An example of this isGabriel's Horn . - ...that the primality of a number can be determined using only a single division using
Wilson's Theorem ? - ...that the line separating the
numerator anddenominator of afraction is called aif written as a diagonal line or asolidus if written as a horizontal line?vinculum - ...that a monkey hitting keys at
random on a typewriter keyboard for an infinite amount of time willalmost surely type the complete works of William Shakespeare? - ... that there are 115,200 solutions to the
ofménage problem permuting six female-male couples at a twelve-person table so that men and women alternate and are seated away from their partners? - ... that
mathematician Paul Erdős called the, a still-open generalization of theHadwiger conjecture four-color problem , "one of the deepest unsolved problems ingraph theory "?

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General | Foundations | Number theory | Discrete mathematics |
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