Distances

The distance between two points is the length of a straight line segment between them. In the case of two locations on Earth, usually the distance along the surface is meant: either "as the crow flies" (along a great circle) or by road, railroad, etc. Distance is sometimes expressed in terms of the time to cover it, for example walking or by car. Sometimes a distance thus indicated is ambiguous because the means of transport is neither mentioned nor obvious.

Distance as mentioned above is sometimes not symmetric, hence not a metric (see below): this applies to distance by car in the case of one-way streets, and also in the case the distance is expressed in terms of the time to cover it (a road may be more crowded in one direction than in the other, for a ship upstream and downstream makes a difference).

As opposed to a position coordinate, a distance can not be negative. Distance is a scalar quantity, containing only a magnitude, whereas displacement is an equivalent vector quantity containing both magnitude and direction.

In the study of complicated geometries, we call the most common type of distance Euclidean distance, as we define it from the Pythagorean theorem.