Coordinate system

related topics
{math, energy, light}
{math, number, function}
{area, part, region}
{language, word, form}

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element.[1][2] The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in 'the x-coordinate'. In elementary mathematics the coordinates are taken to be real numbers, but in more advanced applications coordinates can be taken to be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the bases of analytic geometry.[3]

An example in everyday use is the system of assigning longitude and latitude to geographical locations. In physics, a coordinate system used to describe points in space is called a frame of reference.


Number line

The simplest example of a coordinate system is the identification of points on a line with real numbers using the number line. In this system, an arbitrary point O (the origin) is chosen on a given line. The coordinate of a point P is defined as the signed distance from O to P, where the signed distance is the distance taken as positive or negative depending on which side of the line P lies. Each point is given a unique coordinate and each real number is the coordinate of a unique point.[4]

Full article ▸

related documents
Divergence theorem
Novikov self-consistency principle
Dual polyhedron
Quantization (physics)
Discrete element method
Nonlinear system
Root mean square
Curl (mathematics)
Equations of motion
List of letters used in mathematics and science
Quantum Hall effect
Double pendulum
Horizontal coordinate system
Gauss–Bonnet theorem
Hoag's Object
Nemesis (star)
Principle of relativity
Astronomical distance
Maximum power theorem
Mirror image
Ring Nebula
South Atlantic Anomaly
Universal joint