All Topics  
Three-dimensional space

 

 
   Email Print
   Bookmark   Link
 

 

Three-dimensional space
 
 
  Topics Three-dimensional space Topic Home

Three-dimensional space is a geometric model of the physical universe
Universe

The universe is defined as everything that physically exists: the entirety of space and time, all forms of matter, energy and momentum, and the physical laws and physical constants that govern them....
 in which we live. The three dimensions are commonly called length, width, and depth (or height), although any three mutually perpendicular directions can serve as the three dimensions.

In physics, our three-dimensional space is viewed as embedded in 4-dimensional space-time, called Minkowski space
Minkowski space

In physics and mathematics, Minkowski space is the mathematical setting in which Albert Einstein theory of special relativity is most conveniently formulated....
 (see special relativity
Special relativity

Special relativity is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "Annus Mirabilis Papers#Special relativity"....
).






Discussion
Ask a question about 'Three-dimensional space'
Start a new discussion about 'Three-dimensional space'
Answer questions from other users
Full Discussion Forum



Encyclopedia


Coord Planes Color
Three-dimensional space is a geometric model of the physical universe
Universe

The universe is defined as everything that physically exists: the entirety of space and time, all forms of matter, energy and momentum, and the physical laws and physical constants that govern them....
 in which we live. The three dimensions are commonly called length, width, and depth (or height), although any three mutually perpendicular directions can serve as the three dimensions.

In physics, our three-dimensional space is viewed as embedded in 4-dimensional space-time, called Minkowski space
Minkowski space

In physics and mathematics, Minkowski space is the mathematical setting in which Albert Einstein theory of special relativity is most conveniently formulated....
 (see special relativity
Special relativity

Special relativity is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "Annus Mirabilis Papers#Special relativity"....
). The idea behind space-time is that time is hyperbolic-orthogonal
Hyperbolic-orthogonal

In mathematics, two points in the Cartesian plane are hyperbolically orthogonal if the slopes of their rays from the origin are reciprocal to one another....
 to each of the three spatial dimensions.

In mathematics, Cartesian geometry (analytic geometry
Analytic geometry

Analytic geometry, usually called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra; the modern development of analytic geometry is thus suggestively called algebraic geometry....
) describes every point in three-dimensional space by means of three coordinates. Three Coordinate axes are given, each perpendicular to the other two at the origin
Origin

Origin is a word meaning "beginning." In this sense, it may refer to:*Origin , the beginning, starting-point, cause, or ultimate source, from which a thing is derived;...
, the point at which they cross. They are usually labeled x, y, and z. Relative to these axes, the position of any point in three-dimensional space is given by an ordered triple of real numbers, each number giving the distance of that point from the origin
Origin

Origin is a word meaning "beginning." In this sense, it may refer to:*Origin , the beginning, starting-point, cause, or ultimate source, from which a thing is derived;...
 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 three-dimensional space include cylindrical coordinates and spherical coordinates, though there are an infinite number of possible methods. See Euclidean space
Euclidean space

Around 300 Before Christ, the Ancient Greece mathematician Euclid undertook a study of relationships among distances and angles, first in a plane and then in space....
.

Another mathematical way of viewing three-dimensional space is found in linear algebra
Linear algebra

Linear algebra is the branch of mathematics concerned with the study of Euclidean vectors, vector spaces , linear maps , and system of linear equations....
, 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 three dimensional because every point in space can be described by a linear combination of three independent vector
Coordinate vector

In linear algebra, a coordinate vector is an explicit representation of a vector in an Real_coordinate_space#Intuitive_overview as an ordered list of numbers or, equivalently, as an element of the coordinate space Fn....
s. In this view, space-time is four dimensional because the location of a point in time is independent of its location in space.

Three-dimensional space has a number of properties that distinguish it from spaces of other dimensions. It is, for example, the smallest dimension in which it is possible to tie a knot
Knot theory

In mathematics, knot theory is the area of topology that studies knot s. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs drastically in that the ends are joined together to prevent it from becoming undone....
 in a piece of string . Many of the laws of physics, such as the various inverse square laws, depend on dimension three .

The understanding of three-dimensional space in humans is thought to be learned during infancy using unconscious inference
Visual perception

Visual perception is the ability to interpret information from visible light reaching the eye. The resulting perception is also known as eyesight, sight or vision....
, and is closely related to hand-eye coordination. The visual ability to perceive the world in three dimensions is called depth perception
Depth perception

Depth perception is the visual perception ability to perceive the world in three dimensions. Although any animal capable of moving around its environment must be able to sense the distance of objects in that environment, the term perception is reserved for humans, who are the only beings that can tell each other about their qualia of dist...
.

See also

  • two-dimensional space
  • four-dimensional space
  • Three-dimensional graph
    Three-dimensional graph

    A three-dimensional graph is the graph of a function of a function of two variables f.Provided that x, y, and f are real numbers, the graph can be represented as a plane of curved surface in a Three-dimensional space Cartesian coordinate system....