Euclidean space

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

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