Euclidean space

Euclidean space is the space Euclidean geometry uses. In essence, it is described in Euclid's "Elements". The Euclidean plane (formula_1) and three-dimensional space (formula_2) are part of Euclidean space, which can be generalized to any dimension "n" (in which case one writes formula_3). 
Euclidian space is sometimes called Cartesian space. A few other spaces and mathematical objects that are similar were added later. Euclid based his work "Elements" on certain axioms. Euclidean space can be described using such axioms.