Euclidean space

(redirected from Euclidean 3-space)
Also found in: Thesaurus, Encyclopedia.
Related to Euclidean 3-space: N-dimensional Euclidean space

Euclid′ean space′

ordinary two- or three-dimensional space.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.Euclidean space - a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional
metric space - a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality
euklidovský prostor
espacio euclideoespacio euclídeoespacio euclidiano
euklidinen avaruus
euklidski prostor
euklidiskt rum
References in periodicals archive ?
0] being the outward manifestation in our proper Euclidean 3-space [SIGMA]' of the intrinsic rest mass [phi][m.
van-Brunt, Congruent characteristics on linear Weingarten surfaces in Euclidean 3-space, New Zealand J.
3]([alpha]) is the Lorentz boost along the z-axis with speed [upsilon] = c tanh [alpha]; 0 [less than or equal to] [alpha] [less than or equal to] [infinity], and the Euler angles for rotation in the Euclidean 3-space have their usual finite ranges.
van-Brunt: Congruent characteristic on linear Weingarten surfaces in Euclidean 3-space, New Zeland J.
Here using the standard coordinate system of Euclidean 3-space [E.
Affine translation surfaces in Huili LIU and Yanhua YU Euclidean 3-space On the equivalence of several Shintaro KUROKI and Li YU definitions of compact infra- solvmanifolds Duc Tai PHO Alexander polynomials of certain Above three, communicated by dual of smooth quartics Kenji FUKAYA, M.
At least for their shapes, one can say that constant slope surfaces are one of the most fascinated surfaces in Euclidean 3-space.
Graphically, let us consider the Euclidean 3-space [SIGMA]' with mutually orthogonal straight line dimensions [x.
Ro studied tubes of (X,Y)-Weingarten type in Euclidean 3-space, where X,Y [member of] {K, H, [K.
It is well-known that the classical Weierstrass-Enneper representation formula describes minimal surfaces in Euclidean 3-space [R.
They all have well-behaved distance functions which give rise to the curvature of the space and these curved spaces provide the link to understanding such geometrical ideas as geodesics, curvature, topology, embedded surfaces in Euclidean 3-space, and abstract surfaces with Riemannian metrics.