Euclidean space
1
7.6
- 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?
- What is Hilbert's space and Euclidean space?
- For instance, can you find a Euclidean space, a straight space?
Examples
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It says that given a function that maps a convex and compact subset of the Euclidean space to itself.
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For instance, can you find a Euclidean space, a straight space?
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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.
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The principles of geometry apply universally in Euclidean space, where the shortest distance between two points is a straight line.
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To visualize concepts in geometry, students often use Euclidean space to understand shapes and their properties.
Surface Forms
Morphology
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.