# Perspective

*with centre *

A mapping of a plane into a plane under which each point in is put into correspondence with the point of intersection of the straight line with (if is not parallel to , see Fig.).

Figure: p072410a

More generally, let and be proper subspaces of identical dimension in a projective space and let be a subspace of maximal dimension not having points in common with or . Let be a subspace contained in , let be the subspace of minimal dimension containing and and let be the intersection of and .

The correspondence by which each subspace contained in is put into correspondence with the subspace contained in is called a perspective mapping from into with perspective centre .

A perspective is a collineation. If the subspaces and intersect, then each point in the subspace corresponds to itself.

If projective coordinates are introduced into the spaces and , then a perspective correspondence can be specified by a linear mapping.

#### References

[1] | E. Artin, "Geometric algebra" , Interscience (1957) |

[2] | N.A. Glagolev, "Projective geometry" , Moscow (1963) (In Russian) |

#### Comments

Perspective mappings are also called central projections or perspectivities.

#### References

[a1] | M. Berger, "Geometry" , I , Springer (1987) |

[a2] | H. Busemann, P.J. Kelly, "Projective geometry and projective metrics" , Acad. Press (1953) |

[a3] | H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963) |

[a4] | H.S.M. Coxeter, "Projective geometry" , Blaisdell (1964) |

[a5] | H.S.M. Coxeter, "The real projective plane" , McGraw-Hill (1949) |

**How to Cite This Entry:**

Perspective.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Perspective&oldid=18072