For n equal to one or two, they are commonly called respectively Euclidean lines and Euclidean planes. Originally, that is, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spaces when one wants to specify their dimension. Fundamental space of geometry A point in three-dimensional Euclidean space can be located by three coordinates.Įuclidean space is the fundamental space of geometry, intended to represent physical space.
