# 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]

Euclidian 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]

## References

1. "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-10-12.
2. Weisstein, Eric W. "Euclidean Space". mathworld.wolfram.com. Retrieved 2020-10-12.
3. "Euclidean space | geometry". Encyclopedia Britannica. Retrieved 2020-10-12.