Origin (mathematics)
Inmathematics,theoriginof aEuclidean spaceis a specialpoint,usually denoted by the letterO,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 ofgeometric symmetry.
Cartesian coordinates
[edit]In aCartesian coordinate system,the origin is the point where theaxesof the system intersect.[1]The origin divides each of these axes into two halves, a positive and a negative semiaxis.[2]Points can then be located with reference to the origin by giving their numericalcoordinates—that is, the positions of their projections along each axis, either in the positive or negative direction. The coordinates of the origin are always all zero, for example (0,0) in two dimensions and (0,0,0) in three.[1]
Other coordinate systems
[edit]In apolar 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 positivex-axis and the ray from the origin to the point, and this ray is not well-defined for the origin itself.[3]
InEuclidean geometry,the origin may be chosen freely as any convenient point of reference.[4]
The origin of thecomplex planecan be referred as the point wherereal axisandimaginary axisintersect each other. In other words, it is thecomplex numberzero.[5]
See also
[edit]- 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
[edit]- ^abMadsen, David A. (2001),Engineering Drawing and Design,Delmar drafting series, Thompson Learning, p. 120,ISBN9780766816343.
- ^Pontrjagin, Lev S.(1984),Learning higher mathematics,Springer series in Soviet mathematics, Springer-Verlag, p. 73,ISBN9783540123514.
- ^Tanton, James Stuart (2005),Encyclopedia of Mathematics,Infobase Publishing,ISBN9780816051243.
- ^Lee, John M. (2013),Axiomatic Geometry,Pure and Applied Undergraduate Texts, vol. 21, American Mathematical Society, p. 134,ISBN9780821884782.
- ^Gonzalez, Mario (1991),Classical Complex Analysis,Chapman & Hall Pure and Applied Mathematics, CRC Press,ISBN9780824784157.