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It is possible to define a number of different metrics (measures of distance) on a space and the formula will depend on the metric.

A simple pair of metrics to illustrate: imagine a town with a road layout like downtown Manhattan. Streets and Avenues at right angles to one another. The distance from one corner to another is a number of avenues across plus a number of streets up (or down). This is known as the taxicab or Minkowski metric. An alternative measure is a "as-the-crow-flies" distance. Both measures are perfectly valid but will give rise to different formulae. There are other metric, too.

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