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# Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. 

75 relations: Absolute angular momentum, Alphanumeric grid, Analytic geometry, Arc length, Atlas (topology), Axes conventions, Barycentric coordinate system, Bijection, Cambridge University Press, Canonical coordinates, Cartesian coordinate system, Celestial coordinate system, Cengage, Cesàro equation, Commutative ring, Complex number, Coordinate system, Coordinate-free, Curvature, Curvilinear coordinates, Daniel Pedoe, Differentiable manifold, Dimension, Duality (mathematics), Eddington–Finkelstein coordinates, Elementary mathematics, Euclidean space, Fractional coordinates, Frame of reference, Galilean transformation, Gaussian polar coordinates, Generalized coordinates, Geographic coordinate system, Geometry, Gullstrand–Painlevé coordinates, Hamiltonian mechanics, Herman Feshbach, Homeomorphism, Homogeneous coordinates, Infinity, Intrinsic equation, Isotropic coordinates, Kinematics, Kruskal–Szekeres coordinates, Lagrangian mechanics, Line (geometry), Line coordinates, Log-polar coordinates, Manifold, Matrix (mathematics), ... Expand index (25 more) »

## Absolute angular momentum

In meteorology, absolute angular momentum refers to the angular momentum in an 'absolute' coordinate system (absolute time and space).

## Alphanumeric grid

An alphanumeric grid (also known as atlas grid) is a simple coordinate system on a grid in which each cell is identified by a combination of a letter and a number.

## Analytic geometry

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.

## Arc length

Determining the length of an irregular arc segment is also called rectification of a curve.

## Atlas (topology)

In mathematics, particularly topology, one describes a manifold using an atlas.

## Axes conventions

In ballistics and flight dynamics, axes conventions are standardized ways of establishing the location and orientation of coordinate axes for use as a frame of reference.

## Barycentric coordinate system

In geometry, the barycentric coordinate system is a coordinate system in which the location of a point of a simplex (a triangle, tetrahedron, etc.) is specified as the center of mass, or barycenter, of usually unequal masses placed at its vertices.

## Bijection

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

## Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

## Canonical coordinates

In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time.

## Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

## Celestial coordinate system

In astronomy, a celestial coordinate system is a system for specifying positions of celestial objects: satellites, planets, stars, galaxies, and so on.

## Cengage

Cengage is an educational content, technology, and services company for the higher education, K-12, professional, and library markets worldwide.

## Cesàro equation

In geometry, the Cesàro equation of a plane curve is an equation relating the curvature (\kappa) at a point of the curve to the arc length (s) from the start of the curve to the given point.

## Commutative ring

In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.

## Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

## Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

## Coordinate-free

A coordinate-free, or component-free, treatment of a scientific theory or mathematical topic develops its concepts on any form of manifold without reference to any particular coordinate system.

## Curvature

In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.

## Curvilinear coordinates

In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved.

## Daniel Pedoe

Dan Pedoe (29 October 1910, London – 27 October 1998, St Paul, Minnesota, USA) was an English-born mathematician and geometer with a career spanning more than sixty years.

## Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

## Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

## Duality (mathematics)

In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself.

## Eddington–Finkelstein coordinates

In general relativity, Eddington–Finkelstein coordinates are a pair of coordinate systems for a Schwarzschild geometry (i.e. a spherically symmetric black hole) which are adapted to radial null geodesics.

## Elementary mathematics

Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels.

## Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

## Fractional coordinates

In crystallography, a fractional coordinate system is a coordinate system in which the edges of the unit cell are used as the basic vectors to describe the positions of atomic nuclei.

## Frame of reference

In physics, a frame of reference (or reference frame) consists of an abstract coordinate system and the set of physical reference points that uniquely fix (locate and orient) the coordinate system and standardize measurements.

## Galilean transformation

In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics.

## Gaussian polar coordinates

In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres.

## Generalized coordinates

In analytical mechanics, specifically the study of the rigid body dynamics of multibody systems, the term generalized coordinates refers to the parameters that describe the configuration of the system relative to some reference configuration.

## Geographic coordinate system

A geographic coordinate system is a coordinate system used in geography that enables every location on Earth to be specified by a set of numbers, letters or symbols.

## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

## Gullstrand–Painlevé coordinates

Gullstrand–Painlevé coordinates are a particular set of coordinates for the Schwarzschild metric – a solution to the Einstein field equations which describes a black hole.

## Hamiltonian mechanics

Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.

## Herman Feshbach

Herman Feshbach (February 2, 1917, in New York City – 22 December, 2000, in Cambridge, Massachusetts) was an American physicist.

## Homeomorphism

In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.

## Homogeneous coordinates

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry.

## Infinity

Infinity (symbol) is a concept describing something without any bound or larger than any natural number.

## Intrinsic equation

In geometry, an intrinsic equation of a curve is an equation that defines the curve using a relation between the curve's intrinsic properties, that is, properties that do not depend on the location and possibly the orientation of the curve.

## Isotropic coordinates

In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres.

## Kinematics

Kinematics is a branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the mass of each or the forces that caused the motion.

## Kruskal–Szekeres coordinates

In general relativity Kruskal–Szekeres coordinates, named after Martin Kruskal and George Szekeres, are a coordinate system for the Schwarzschild geometry for a black hole.

## Lagrangian mechanics

Lagrangian mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788.

## Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

## Line coordinates

In geometry, line coordinates are used to specify the position of a line just as point coordinates (or simply coordinates) are used to specify the position of a point.

## Log-polar coordinates

In mathematics, log-polar coordinates (or logarithmic polar coordinates) is a coordinate system in two dimensions, where a point is identified by two numbers, one for the logarithm of the distance to a certain point, and one for an angle.

## Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

## Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

## Nomogram

A nomogram (from Greek νόμος nomos, "law" and γραμμή grammē, "line"), also called a nomograph, alignment chart or abaque, is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function.

## Number

A number is a mathematical object used to count, measure and also label.

## Orientation (geometry)

In geometry the orientation, angular position, or attitude of an object such as a line, plane or rigid body is part of the description of how it is placed in the space it occupies.

## Orthogonal coordinates

In mathematics, orthogonal coordinates are defined as a set of d coordinates q.

## Perpendicular

In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).

## Philip M. Morse

Philip McCord Morse (August 6, 19035 September 1985), was an American physicist, administrator and pioneer of operations research (OR) in World War II.

## Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

## Plücker coordinates

In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective 3-space, P3.

## Point (geometry)

In modern mathematics, a point refers usually to an element of some set called a space.

## Projective plane

In mathematics, a projective plane is a geometric structure that extends the concept of a plane.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

## Right-hand rule

In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation conventions for the vector cross product in three dimensions.

## Rigid body

In physics, a rigid body is a solid body in which deformation is zero or so small it can be neglected.

## Rotation of axes

In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the origin is kept fixed and the x' and y' axes are obtained by rotating the x and y axes counterclockwise through an angle \theta.

## Schwarzschild coordinates

In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres.

## Skew coordinates

A system of skew coordinates is a curvilinear coordinate system where the coordinate surfaces are not orthogonal, in contrast to orthogonal coordinates.

## Spherical coordinate system

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.

## Tangential angle

In geometry, the tangential angle of a curve in the Cartesian plane, at a specific point, is the angle between the tangent line to the curve at the given point and the -axis.

## Ternary plot

A ternary plot, ternary graph, triangle plot, simplex plot, Gibbs triangle or de Finetti diagram is a barycentric plot on three variables which sum to a constant.

## Translation of axes

In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away.

## Triangle

A triangle is a polygon with three edges and three vertices.

## Trilinear coordinates

In geometry, the trilinear coordinates x:y:z of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle.

## Tuple

In mathematics, a tuple is a finite ordered list (sequence) of elements.

## Unit vector

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

## Whewell equation

The Whewell equation of a plane curve is an equation that relates the tangential angle (\varphi) with arclength (s), where the tangential angle is the angle between the tangent to the curve and the x-axis, and the arc length is the distance along the curve from a fixed point.

## References

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