the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space. More general three-dimensional spaces...
34 KB (4,829 words) - 01:43, 17 April 2024
Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible...
45 KB (5,487 words) - 22:30, 11 April 2024
plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space R 3 {\displaystyle...
14 KB (2,457 words) - 15:09, 17 April 2024
A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because...
34 KB (3,894 words) - 00:48, 1 April 2024
five-dimensional space is a space with five dimensions. In mathematics, a sequence of N numbers can represent a location in an N-dimensional space. If...
15 KB (1,613 words) - 12:36, 9 May 2024
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional space...
47 KB (6,957 words) - 21:59, 2 May 2024
dimensions. Although the space we live in is considered three-dimensional, there are practical applications for four-dimensional space. Quaternions, one of...
14 KB (2,020 words) - 00:58, 17 April 2024
Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions...
34 KB (4,294 words) - 17:27, 16 May 2024
Euclidean plane (redirect from Euclidean two-dimensional space)
plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space R 3 {\displaystyle...
16 KB (1,963 words) - 04:54, 30 April 2024
finite-dimensional if the dimension of V {\displaystyle V} is finite, and infinite-dimensional if its dimension is infinite. The dimension of the vector space V {\displaystyle...
9 KB (1,485 words) - 00:27, 14 May 2024
Plane (mathematics) (redirect from Planar space)
dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is...
6 KB (1,516 words) - 15:13, 17 April 2024
A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described...
7 KB (761 words) - 02:15, 31 December 2023
In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several...
4 KB (437 words) - 09:04, 11 April 2024
Three-dimensional chess (or 3‑D chess) is any chess variant that replaces the two-dimensional board with a three-dimensional array of cells between which...
17 KB (1,817 words) - 22:11, 17 May 2024
also refer to a seven-dimensional manifold such as a 7-sphere, or a variety of other geometric constructions. Seven-dimensional spaces have a number of special...
5 KB (499 words) - 20:44, 15 November 2020
3-sphere (redirect from Three-dimensional sphere)
3-sphere, glome or hypersphere is a higher-dimensional analogue of a sphere. In 4-dimensional Euclidean space, it is the set of points equidistant from...
28 KB (4,000 words) - 05:53, 7 May 2024
Spacetime (redirect from Space-time interval)
mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are...
198 KB (27,819 words) - 08:35, 10 May 2024
in n-dimensional space. When n = 8, the set of all such locations is called 8-dimensional space. Often such spaces are studied as vector spaces, without...
7 KB (718 words) - 02:52, 3 July 2022
Any straight line or smooth curve is a one-dimensional space, regardless of the dimension of the ambient space in which the line or curve is embedded. Examples...
3 KB (377 words) - 09:59, 13 February 2024
3-manifold (redirect from Three-dimensional manifold)
mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible...
45 KB (5,836 words) - 09:37, 24 April 2024
space of a manifold is a generalization of tangent lines to curves in two-dimensional space and tangent planes to surfaces in three-dimensional space...
19 KB (3,167 words) - 10:30, 6 November 2023
dimension is an infinite cardinal. Finite-dimensional vector spaces occur naturally in geometry and related areas. Infinite-dimensional vector spaces...
88 KB (11,542 words) - 07:19, 25 April 2024
be used for indicating sides (e.g., interior or exterior). In three-dimensional space, a surface normal, or simply normal, to a surface at point P is...
15 KB (2,452 words) - 00:50, 20 April 2024
Euclidean space of dimension n, En (Euclidean line, E; Euclidean plane, E2; Euclidean three-dimensional space, E3) form a real coordinate space of dimension n...
31 KB (4,248 words) - 13:58, 12 February 2024
of a coordinate frame attached to a rigid body in three-dimensional space form its configuration space, often denoted R 3 × S O ( 3 ) {\displaystyle \mathbb...
10 KB (1,410 words) - 07:45, 25 November 2023
This system maps the space of lines in three-dimensional space to projective space RP5, but with the additional requirement the space of lines corresponds...
10 KB (1,608 words) - 12:20, 8 November 2023
Solid geometry (redirect from Three-dimensional geometry)
the geometry of three-dimensional Euclidean space (3D space). A solid figure is the region of 3D space bounded by a two-dimensional surface; for example...
8 KB (374 words) - 23:49, 18 April 2024
Klein bottle (category Topological spaces)
The Klein bottle can be constructed (in a four dimensional space, because in three dimensional space it cannot be done without allowing the surface to...
20 KB (2,907 words) - 01:28, 2 April 2024
A three-dimensional graph may refer to A graph (discrete mathematics), embedded into a three-dimensional space The graph of a function of two variables...
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Geometry (redirect from Geometrical space)
geometry led to a change of meaning of the word "space", which originally referred to the three-dimensional space of the physical world and its model provided...
100 KB (9,874 words) - 08:58, 6 May 2024