Page "Metric space" Paragraph 1

The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space.

In fact, the notion of " metric " is a generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance.

The Euclidean metric defines the distance between two points as the length of the straight line segment connecting them.

Other metric spaces occur for example in elliptic geometry and hyperbolic geometry, where distance on a sphere measured by angle is a metric, and the hyperboloid model of hyperbolic geometry is used by special relativity as a metric space of velocities.