distance <geometry, metric spaces>
minimal length of a curve that joins the two points or geometries
Note to entry: The usual distance function for two points in a coordinate space assumes an underlying plane and is a Euclidean distance. If the underlying Reference Surface is not a plane, then distance is defined by this minimum length of all curves between the two points. These surfaces are prime examples of non-Euclidean geometry, where the parallel postulate in Euclid's Elements does not hold. In mathematical terms, distance is the "greatest lower bound" of the length of the curves. The word minimum is sometimes used, but there should be no expectation that an instance of that minimum actually occurs, only that any larger number will have a length in the set that is smaller.
ORIGIN: ISO/TC 211 Glossary of Terms - English (last updated: 2020-06-02)