Point

A spatial point is an entity with a location in space but no extent (volume, area or length). In geometry, a point therefore captures the notion of location; no further information is captured. Points are used in the basic language of geometry, physics, vector graphics (both 2d and 3d), and many other fields. In mathematics generally, any form of space is considered as made up of points as basic elements.

Points in Euclidean geometry

A point in Euclidean geometry has no size, orientation, or any other feature except position. Euclid's axioms or postulates assert in some cases that points exist: for example, they assert that if two lines on a plane are not parallel, there is exactly one point that lies on both of them.

Points in Cartesian geometry

Intuitively one can understand a location in 3d space. This location could be described with three real number coordinates: for instance

P = (2, 6, 9)

But one can also describe points in 1, 2 or more than 3 dimensions.

The description of a point is quite similar to the description of a spatial vector, which also can exist in space with dimensions from one to many. The conceptual difference between these notions is significant, though: a point indicates a location, while a vector indicates a direction and length. If a distinguished point (the origin) is given, one can describe a location by giving the direction and distance from the origin to that point.

See also