Euclidean space

noun

, Mathematics.

1. ordinary two- or three-dimensional space.
2. any vector space on which a real-valued inner product is defined.

Word History and Origins

Origin of Euclidean space¹

First recorded in 1880–85

Example Sentences

For example, in linear algebra one studies abstract vector spaces such as three-dimensional Euclidean space.

From Scientific American

In Euclidean space, staring at a point at infinity means that the lines of sight of the two eyes track parallel lines.

From Nature

Russell Markert’s original choreography makes abstraction mesmerizingly beautiful as it puts the Euclidean space in motion.

From New York Times

In Euclidean space, equilateral triangles have 60 degree angles, so the only way to fit them together in the plane is to put six of them around one point.

From Scientific American

The 'extrinsic' approach views them in 'Euclidean space', rather like plotting them against the familiar axes of graphs — for example a sphere is the surface of a three-dimensional ball.

From Nature