Möbius transformation cross-ratio preservation theorem

A Möbius transformationMathworldPlanetmath f:zw preserves the cross-ratios, i.e.


Conversely, given two quadruplets which have the same cross-ratioMathworldPlanetmath, there exists a Möbius transformation which maps one quadruplet to the other.

A consequence of this result is that the cross-ratio of (a,b,c,d) is the value at a of the Möbius transformation that takes b, c, d, to 1, 0, respectively.

Title Möbius transformation cross-ratio preservation theorem
Canonical name MobiusTransformationCrossratioPreservationTheorem
Date of creation 2013-03-22 13:35:50
Last modified on 2013-03-22 13:35:50
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 9
Author rspuzio (6075)
Entry type Theorem
Classification msc 30E20
Related topic CrossRatio