Euclidean space

Euclidean space is the space Euclidean geometry uses. In essence, it is described in Euclid's Elements. The Euclidean plane (${\displaystyle \mathbb {R} ^{2}}$) and three-dimensional space (${\displaystyle \mathbb {R} ^{3}}$) are part of Euclidean space, which can be generalized to any dimension n (in which case one writes ${\displaystyle \mathbb {R} ^{n}}$).^[1]

Euclidean space is sometimes called Cartesian space.^[2] 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.^[3]

Related pages

• Elliptic geometry
• Hyperbolic geometry