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Strangely enough, there are many definitions!

In the Euclidean plane, the distance between any two points is the length of the straight line joining those points. This is the concept of distance most commonly used.

However, day-to-day distances are often measured, not "as the crow flies", but along established roads or routes. Here, the distance between two points is the sum of point-to-point distances of straight line segments. An interesting variation is the metric variously known as Minkovski, Manhattan or Taxicab metric. Here the idea is that the distance between two points is the sum of their North-South separation and their East-West separation. See link for more.

In three dimensional space, such as on the surface of the earth, distance is measured not along a straight line but along the arc of the appropriate great circle (see link for more).

There is a whole branch of mathematics - metric spaces - which is the study of spaces with different metrics (or ways of measuring distance) defined for them.

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12y ago

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