Ads
related to: 3 dimensional geometry
Search results
Results from the WOW.Com Content Network
In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space.
Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space). [1] A solid figure is the region of 3D space bounded by a two-dimensional closed surface ; for example, a solid ball consists of a sphere and its interior .
The three possible plane-line relationships in three dimensions. (Shown in each case is only a portion of the plane, which extends infinitely far.) In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line. It is the entire line if that line is embedded in the plane, and is ...
This representation is a higher-dimensional analog of the gnomonic projection, mapping unit quaternions from a 3-sphere onto the 3-dimensional pure-vector hyperplane. It has a discontinuity at 180° (π radians): as any rotation vector r tends to an angle of π radians, its tangent tends to infinity.
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, 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 n, which are called Euclidean n-spaces when one wants to specify their ...
In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space. A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimal thin.
The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language. [1]
Traditional geometry allowed dimensions 1 (a line or curve), 2 (a plane or surface), and 3 (our ambient world conceived of as three-dimensional space). Furthermore, mathematicians and physicists have used higher dimensions for nearly two centuries. [ 71 ]
Ads
related to: 3 dimensional geometry