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...ite inner product; an element of a Euclidean vector space. In [[physics]], euclidean vectors are used to represent [[physical]] [[quantities]] that have both ma ...wiki/Euclidean_space Euclidean space], producing a third three-dimensional Euclidean vector

...t is of a different sort than the spatial dimensions. According to certain Euclidean space [[perception]]s, the [[universe]] has three [[dimension]]s of [[space In [[classical mechanics]], the use of Euclidean space instead of spacetime is appropriate, as time is treated as [[universa

...ht, as in the setting of [https://en.wikipedia.org/wiki/Euclidean_geometry Euclidean geometry]. When [[working]] in two-dimensional Euclidean space, the definite article is used, the plane, to refer to the whole [[spa

...ut into an axiomatic form by [[Euclid]], whose treatment set forth in his [Euclidean geometry]] became a standard for many centuries to follow. The field of [[a ...rs manifolds, spaces that are considerably more abstract than the familiar Euclidean [[space]], which they only approximately resemble at small scales. These sp

...ane (i.e. a two-dimensional [https://en.wikipedia.org/wiki/Euclidean_space Euclidean space]).

...t is of a different sort than the spatial dimensions. According to certain Euclidean [[space]] [[perception]]s, the [[universe]] has three dimensions of space a In classical mechanics, the use of Euclidean space instead of spacetime is appropriate, as time is treated as universal

...and curves in n-dimensional [https://en.wikipedia.org/wiki/Euclidean_space Euclidean space].

...l space. When n = 3, the set of all such locations is called 3-dimensional Euclidean space. It is commonly represented by the symbol [[File:R-3-2.jpg]] . This s

''[[Euclidean space|Space]]'', as we perceive it, is three-dimensional. We can think of p ...[Norm (mathematics)|normed]] [[Normed vector space|vector space]] with the Euclidean norm. The "length" of a vector

...c [[geometry]], such as the [https://en.wikipedia.org/wiki/Euclidean_plane Euclidean] or projective planes, or as [[abstract]] incidence [[structures]]. In the

...f this triangle, and the less the visual angle. This follows simply from [[Euclidean geometry]].

...y a [[Euclidean space]] can be seen as generalizations of the concept of a Euclidean coordinate system. Important varieties of vector spaces with more imposed s

...ct at right angles. Because of this feature, distances between points in a Euclidean space are easy to calculate from their Cartesian cooridnates: If point p ha ...], Cartesian coordinates do not exist. It turns out that for a space to be Euclidean is just for the space to admit of Cartesian coordinates. That is, the dista

...ed to be a two-dimensional spherical surface embedded in three-dimensional Euclidean space, while a ball is a solid figure bounded by a sphere.

...ch makes certain calculations easy; in fact most [[linear operator]]s on [[Euclidean space]] take on a simpler form when written as a matrix relative to some ba

...t in all such objects in [https://en.wikipedia.org/wiki/Euclidean_geometry Euclidean geometry]. Although my amplification has the [[virtue]] of bringing rotatio