Euclidean space

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

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

Template:Math-stub Template:Authority control