Skip to main content
Glite Dictionary
Euclidean space

Euclidean space

1 7.6
A space with flat geometry and a fixed number of dimensions, like a flat plane or room
  • noun
  • /juˈklɪdiən speɪs/
  • Specialized
: espacio euclidiano
  • That is the formula for Euclidean distance on the Euclidean and the Euclidean space for the distance between two points.

What is Hilbert's space and Euclidean space?

Autoplay Next

Examples

  • It says that given a function that maps a convex and compact subset of the Euclidean space to itself.

  • For instance, can you find a Euclidean space, a straight space?

    The Royal Institution

  • But that doesn't affect any geometry theorems operating in our familiar, boring Euclidean space.

    Blog text (24)

  • In this paper, we focus on formal analysis of systems with continuous multi-affine vector fields, i.e., affine in each variable, defined in rectangular regions of the Euclidean space.

    Academic text (2010)

  • In mathematics, we learn that lines in a two-dimensional Euclidean space are straight and can be represented by linear equations.

  • The principles of geometry apply universally in Euclidean space, where the shortest distance between two points is a straight line.

  • To visualize concepts in geometry, students often use Euclidean space to understand shapes and their properties.

Surface Forms

Euclidean space singular
Euclidean spaces plural

Morphology

Euclidean + space

The phrase is directly compositional: 'Euclidean' specifies the type of geometry (flat, Euclid's) and 'space' denotes an area, so together they mean a space governed by Euclidean geometry — a meaning a learner can infer if they know both constituents. Although technical, the adjective+noun construction is predictable and mirrors equivalent terms in many languages, so it is not idiomatic or opaque.

Etymology

Euclidean space is named after Euclid, a Greek teacher who wrote about simple, 'flat' geometry made of straight lines and right angles. So Euclidean space means a mathematical 'space' where those easy rules about straight lines and distance apply, like the flat geometry we learn in school.