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.

---

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

I take the position that the human mind apparently is able to conceptualise Euclidean space - and that this actually defines our concept of space.

From Definition & Reality in the General Theory of Political Economy by Colignatus, Thomas