Euclidean space

American  

noun

Mathematics.

1. ordinary two- or three-dimensional space.

2. any vector space on which a real-valued inner product is defined.

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Etymology

Origin of Euclidean space

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 • Sep. 14, 2021

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

From Nature • Mar. 20, 2017

A few years before Nash, Nirenberg had proved a result for a special case of the same problem, showing that a class of two-dimensional surfaces can be embedded as convex bodies in three-dimensional Euclidean space.

From Nature • Mar. 24, 2015

The surface is not constructible in three-dimensional Euclidean space but has interesting properties, such as being one-sided, like the Möbius strip ...

From The Guardian • Jul. 19, 2012

By positing the point as the unit from which to start, and deriving our conception of the plane from the point, we constitute Euclidean space.

From Man or Matter by Lehrs, Ernst