Euclidean space

Euclidean space is the space Euclidean geometry uses. In essence, it is described in Euclid's Elements. The Euclidean plane (<math>\mathbb{R}^2</math>) and three-dimensional space (<math>\mathbb{R}^3</math>) are part of Euclidean space, which can be generalized to any dimension n (in which case one writes <math>\mathbb{R}^n</math>).

Euclidean 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.

Related pages

• Elliptic geometry
• Hyperbolic geometry

Other websites

• Euclidean Space and Metric Spaces