A space the properties of which are described by the axioms of Euclidean geometry. In a more general sense, a Euclidean space is a finite-dimensional real vector space with an inner product , , which in a suitably chosen (Cartesian) coordinate system
is given by the formula
Sometimes the phrase "Euclidean space" stands for the case , as opposed to the case — Euclidean plane.
See, e.g., [a1], Chapts. 8, 9.
|[a1]||M. Berger, "Geometry" , I , Springer (1987)|
Euclidean space. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Euclidean_space&oldid=13577