# Equi-affine geometry

From Encyclopedia of Mathematics

The branch of affine geometry that studies the invariants of an affine unimodular group of transformations. The most important fact is the existence in equi-affine geometry of areas of parallelograms in plane geometry and of volumes of parallelepipeds in three-dimensional geometry.

#### Comments

See [a1], p. 276; [a2], pp. 150-156; [a3], pp.40-52; [a4]; and [a5], p. 367.

#### References

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

[a2] | M. Spivak, "A comprehensive introduction to differential geometry" , 2 , Publish or Perish pp. 1–5 |

[a3] | L. Fejes Toth, "Lagerungen in der Ebene, auf der Kugel und im Raum" , Springer (1972) |

[a4] | J. Dieudonné, "Treatise on analysis" , 4 , Acad. Press (1974) |

[a5] | W. Blaschke, "Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. Affine Differentialgeometrie" , 2 , Springer (1923) |

**How to Cite This Entry:**

Equi-affine geometry.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Equi-affine_geometry&oldid=34173

This article was adapted from an original article by L.A. Sidorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article