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** Daniel Christopher**^{*}

Department of Mathematics and Statistics, The University of CambridgeÃ¢Â€Â‹, Cambridge, United States

- *Corresponding Author:
- Daniel Christopher

Department of Mathematics and Statistics,

The University of Cambridge,

Cambridge

United States

**E-mail:**Danielchristo12@gmail.edu

** Received:** 15-Mar-2022, Manuscript No. JSMS-22-57473; **Editor assigned:** 17- Mar-2022, Pre QC No. JSMS-22-57473 (PQ); **Reviewed:** 31- Mar-2022, QC No. JSMS-22-57473; **Accepted: **04-Apr-2022, Manuscript No.** **JSMS-22-57473 (A); **Published:** 11-Apr-2022, DOI: 10.4172/ J Stats Math Sci.8.3.004.

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A coordinate system is a geometry system that uses one or more numbers, or coordinates, to uniquely determine the location of points or other geometric components on a manifold, such as Euclidean space. The order of the coordinates is important, and they can be recognized by their position in an ordered tuple or by a letter, as in "the x-coordinate." The coordinates are supposed to be real numbers in fundamental mathematics, although they might be complex numbers or members of a more abstract system like a commutative ring. Analytic geometry is based on the usage of a coordinate system, which allows issues in geometry to be transformed into questions regarding numbers and vice versa.

**Number line**

The simplest example of a coordinate system is the use of a number line to identify points on a line with real numbers. On a given line, an arbitrary point O (the origin) is picked in this system. The coordinate of a point P is the signed distance from O to P, where the signed distance is the distance regarded positive or negative depending on which side of the line P lies. A unique coordinate is assigned to each point, and each real number is the coordinate of a single point.

**Cartesian coordinate system**

The Cartesian coordinate system is a classic example of a coordinate system. Two perpendicular lines are chosen in the plane, and the coordinates of a point are the signed distances between them. Three mutually orthogonal planes are chosen in three dimensions, and the three coordinates of a point are the signed distances between them. Any point in n-dimensional Euclidean space may be given n coordinates using this method.

The three-dimensional system can be right-handed or left-handed depending on the orientation and order of the coordinate axes. This is only one of the numerous coordinate systems accessible.

**Polar coordinate system**

The polar coordinate system is another frequent planar coordinate system. The pole is picked, and the polar axis is determined by a beam emanating from that location. There is a single line across the pole whose angle with the polar axis is for a given angle (measured counter clockwise from the axis to the line). Then, for the given integer r, there is a single point on this line whose signed distance from the origin is r. There is a single point for each pair of coordinates (r, Ãâ ÃÅ¸) however every point is represented by numerous pairs of coordinates.

**Cylindrical and spherical coordinate systems**

The polar coordinate system may be extended to three dimensions using one of two ways. A z-coordinate with the same meaning as in Cartesian coordinates is added to the r and polar coordinates in the cylindrical coordinate system, yielding a triple (r,Ãâ ÃÅ¸, z). Spherical coordinates go even farther by translating the pair of cylindrical coordinates (r, z) to polar coordinates (ρ,ÃÂÃâ¢), yielding a triple (ρ,Ãâ ÃÅ¸,ÃÂÃâ¢).

**Homogeneous coordinate system**

A triple (x, y, z) can be used to represent a point in the plane in homogeneous coordinates, where x/z and y/z are the point's Cartesian coordinates. Because only two coordinates are required to identify a point on the plane, this system provides an "extra" coordinate, but it is beneficial in that it may represent any point on the projective plane without using infinity. In general, a homogeneous coordinate system is one in which only the coordinate ratios, not the actual values, are relevant.