Euclidean space

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

Euclidian 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.

Euclidean Space Media

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  A point in three-dimensional Euclidean space can be located by three coordinates.

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  Positive and negative angles on the oriented plane

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  3-dimensional skew coordinates

Related pages

• Elliptic geometry
• Hyperbolic geometry

Other websites

• Euclidean Space and Metric Spaces