Threedimensional
History of geometry 
Research areas 
Important concepts Point · Line · Perpendicular · Parallel · Line segment · Ray · Plane · Length · Area · Volume · Vertex · Angle · Congruence · Similarity · Polygon · Triangle · Altitude · Hypotenuse · Pythagorean theorem · Quadrilateral · Trapezoid · Kite · Parallelogram (Rhomboid, Rectangle, Rhombus, Square) · Diagonal · Symmetry · Curve · Circle · Area of a disk · Circumference · Diameter · Cylinder · Sphere · Pyramid · Dimensions (one, two, three, four) 
Geometers Aryabhata · Ahmes · Apolonius · Archimedes · Baudhayana · Bolyai · Brahmagupta · Euclid · Pythagoras · Khayyám · Descartes · Pascal · Euler · Gauss · Ibn alYasamin · Jyeṣṭhadeva · Kātyāyana · Lobachevsky · Manava · Minggatu · Riemann · Klein · Parameshvara · Poincaré · Sijzi · Hilbert · Minkowski · Cartan · Veblen · Sakabe Kōhan · Gromov · Atiyah · Virasena · Yang Hui · Yasuaki Aida · Zhang Heng 
Threedimensional space is a geometric 3parameters model of the physical universe (without considering time) in which we exist. These three dimensions can be labeled by a combination of three chosen from the terms length, width, height, depth, and breadth. Any three directions can be chosen, provided that they do not all lie in the same plane.
In physics and mathematics, a sequence of n numbers can be understood as a location in ndimensional space. When n = 3, the set of all such locations is called 3dimensional Euclidean space. It is commonly represented by the symbol $\backslash scriptstyle\{\backslash mathbb\{R\}\}^3$. This space is only one example of a great variety of spaces in three dimensions called 3manifolds.
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In mathematics, analytic geometry (also called Cartesian geometry) describes every point in threedimensional space by means of three coordinates. Three coordinate axes are given, usually each perpendicular to the other two at the origin, the point at which they cross. They are usually labeled x, y, and z. Relative to these axes, the position of any point in threedimensional space is given by an ordered triple of real numbers, each number giving the distance of that point from the origin measured along the given axis, which is equal to the distance of that point from the plane determined by the other two axes.
Other popular methods of describing the location of a point in threedimensional space include cylindrical coordinates and spherical coordinates, though there is an infinite number of possible methods. See Euclidean space.
Another mathematical way of viewing threedimensional space is found in linear algebra, where the idea of independence is crucial. Space has three dimensions because the length of a box is independent of its width or breadth. In the technical language of linear algebra, space is threedimensional because every point in space can be described by a linear combination of three independent vectors. In this view, spacetime is fourdimensional because the location of a point in time is independent of its location in space.
Threedimensional space has a number of properties that distinguish it from spaces of other dimension numbers. For example, at least three dimensions are required to tie a knot in a piece of string.^{[1]} Many of the laws of physics, such as the various inverse square laws, depend on dimension three.^{[2]}
The understanding of threedimensional space in humans is thought to be learned during infancy using unconscious inference, and is closely related to handeye coordination. The visual ability to perceive the world in three dimensions is called depth perception.
With the space $\backslash scriptstyle\{\backslash mathbb\{R\}\}^3$, the topologists locally model all other 3manifolds.
In physics, our threedimensional space is viewed as embedded in fourdimensional spacetime, called Minkowski space (see special relativity). The idea behind spacetime is that time is hyperbolicorthogonal to each of the three spatial dimensions.
Geometry
Polytopes
In three dimensions, there are nine regular polytopes: the five convex Platonic solids and the four nonconvex KeplerPoinsot polyhedra.
Class  Platonic solids  KeplerPoinsot polyhedra  

Symmetry  T_{d}  O_{h}  I_{h}  
Coxeter group  A_{3}  BC_{3}  H_{3}  
Order  24  48  120  
Regular polyhedron 
{3,3}  {4,3}  {3,4}  {5,3}  {3,5}  {5/2,5}  {5,5/2}  {5/2,3}  {3,5/2} 
Hypersphere
A hypersphere in 3space (also called a 2sphere because its surface is 2dimensional) consists of the set of all points in 3space at a fixed distance r from a central point P. The volume enclosed by this surface is:
$V\; =\; \backslash frac\{4\}\{3\}\backslash pi\; r^\{3\}$
Another hypersphere, but having a threedimensional surface is the 3sphere: points equidistant to the origin of the euclidean space $\backslash mathbb\{R\}^4$ at distance one. If any position is $P=(x,y,z,t)$, then $x^2+y^2+z^2+t^2=1$ characterize a point in the 3sphere.
Orthogonality
In the familiar 3dimensional space that we live in, there are three pairs of cardinal directions: up/down (altitude), north/south (latitude), and east/west (longitude). These pairs of directions are mutually orthogonal: They are at right angles to each other. In mathematical terms, they lie on three coordinate axes, usually labelled x, y, and z. The zbuffer in computer graphics refers to this zaxis, representing depth in the 2dimensional imagery displayed on the computer screen.
Coordinate systems
In mathematics, analytic geometry (also called Cartesian geometry) describes every point in threedimensional space by means of three coordinates. Three coordinate axes are given, each perpendicular to the other two at the origin, the point at which they cross. They are usually labeled x, y, and z. Relative to these axes, the position of any point in threedimensional space is given by an ordered triple of real numbers, each number giving the distance of that point from the origin measured along the given axis, which is equal to the distance of that point from the plane determined by the other two 2 axes.
Other popular methods of describing the location of a point in threedimensional space include cylindrical coordinates and spherical coordinates, though there is an infinite number of possible methods. See Euclidean space.
Below are images of the abovementioned systems.
See also
References
External links
Commons has media related to 3D. 
 MathWorld.
 University of Queensland, 1991
