Topology is an abstract form of geometry which is not metric (that is, it takes no account of measurements or sizes). Any forms or figures which can be continuously deformed into each other are treated as equivalent.



A well-known traditional problem of topology is how many different colours you need when drawing a (two-dimensional) map to ensure that no two countries with a common border have the same colour. If you try it, you will see, intuitively, that four colours are enough. But no proof was available of this until recently. The proof requires extensive use of computers, and has encountered some controversy.



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