Definitions for euclidean space
eu·clidean space

Princeton's WordNetRate this definition:0.0 / 0 votes

1. Euclidean spacenoun

   a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional

WiktionaryRate this definition:3.0 / 1 vote

1. Euclidean spacenoun

   Ordinary two- or three-dimensional space, characterised by an infinite extent along each dimension and a constant distance between any pair of parallel lines.

2. Euclidean spacenoun

   Any real vector space on which a real-valued inner product (and, consequently, a metric) is defined.

WikipediaRate this definition:0.0 / 0 votes

1. Euclidean space

   Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension, including the three-dimensional space and the Euclidean plane (dimension two). The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that were later considered in physics and modern mathematics. Ancient Greek geometers introduced Euclidean space for modeling the physical space. Their work was collected by the ancient Greek mathematician Euclid in his Elements, with the great innovation of proving all properties of the space as theorems, by starting from a few fundamental properties, called postulates, which either were considered as evident (for example, there is exactly one straight line passing through two points), or seemed impossible to prove (parallel postulate). After the introduction at the end of 19th century of non-Euclidean geometries, the old postulates were re-formalized to define Euclidean spaces through axiomatic theory. Another definition of Euclidean spaces by means of vector spaces and linear algebra has been shown to be equivalent to the axiomatic definition. It is this definition that is more commonly used in modern mathematics, and detailed in this article. In all definitions, Euclidean spaces consist of points, which are defined only by the properties that they must have for forming a Euclidean space. There is essentially only one Euclidean space of each dimension; that is, all Euclidean spaces of a given dimension are isomorphic. Therefore, in many cases, it is possible to work with a specific Euclidean space, which is generally the real n-space R n , {\displaystyle \mathbb {R} ^{n},} equipped with the dot product. An isomorphism from a Euclidean space to R n {\displaystyle \mathbb {R} ^{n}} associates with each point an n-tuple of real numbers which locate that point in the Euclidean space and are called the Cartesian coordinates of that point.

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1. euclidean space

   Euclidean space is a mathematical concept referring to a two or three-dimensional space in which the laws of Euclidean geometry, named after the ancient Greek mathematician Euclid, apply. These spaces are characterized by having a flat geometry, where the notions of angle, distance, and shape are defined conventionally. In more advanced mathematics, Euclidean space can be generalized to higher dimensions, and is defined as a space with a positive-definite quadratic form. It’s fundamental in physics and engineering for describing physical space.

WikidataRate this definition:0.0 / 0 votes

1. Euclidean space

   In mathematics, particularly in geometry, the concept of an Euclidean space encompasses Euclidean plane and the three-dimensional space of Euclidean geometry as spaces of dimensions 2 and 3 respectively. It is named after the Ancient Greek mathematician Euclid of Alexandria. The term “Euclidean” distinguishes these spaces from other types of spaces considered in modern geometry. Euclidean spaces also generalizes these ideas to higher dimensions. Classical Greek geometry defined the Euclidean plane and Euclidean three-dimensional space using certain postulates, while the other properties of these spaces were deduced as theorems. Geometric constructions also used to define rational numbers. When algebra and mathematical analysis became developed enough, this relation reversed and now it is more common to define Euclidean space using Cartesian coordinates and the ideas of analytic geometry. It means that points of the space are specified with collections of real numbers and geometric shapes are defined as equations and inequalities. This approach brings the tools of algebra and calculus to bear on questions of geometry, and has the advantage that it generalizes easily to Euclidean spaces of more than three dimensions.

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1. • Metric Space

How to pronounce euclidean space?

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How to say euclidean space in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of euclidean space in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of euclidean space in Pythagorean Numerology is: 1

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=euclidean space
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Euclidean_Space
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Euclidean_Space
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=euclidean space