Origin (mathematics)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Coordinate_with_Origin.svg/212px-Coordinate_with_Origin.svg.png)
In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space.
In physical problems, the choice of origin is often arbitrary, meaning any choice of origin will ultimately give the same answer. This allows one to pick an origin point that makes the mathematics as simple as possible, often by taking advantage of some kind of geometric symmetry.
Cartesian coordinates
In a
Other coordinate systems
In a polar coordinate system, the origin may also be called the pole. It does not itself have well-defined polar coordinates, because the polar coordinates of a point include the angle made by the positive x-axis and the ray from the origin to the point, and this ray is not well-defined for the origin itself.[3]
In Euclidean geometry, the origin may be chosen freely as any convenient point of reference.[4]
The origin of the
See also
- Null vector, an analogous point of a vector space
- Distance from a point to a plane
- Pointed space, a topological space with a distinguished point
- Radial basis function, a function depending only on the distance from the origin
References
- ^ ISBN 9780766816343.
- ISBN 9783540123514.
- ISBN 9780816051243.
- ISBN 9780821884782.
- ISBN 9780824784157.