Editing Conformal geometry (section)

====The inversive model====
The inversive model of conformal geometry consists of the group of local transformations on the [[Euclidean space]] '''E'''<sup>''n''</sup> generated by inversion in spheres.  By [[Liouville's theorem (conformal mappings)|Liouville's theorem]], any angle-preserving local (conformal) transformation is of this form.<ref>{{springer|id=L/l059680|title=Liouville theorems|author=S.A. Stepanov}}.  {{cite book|chapter=''Extension au case des trois dimensions de la question du tracé géographique, Note VI'' (by J. Liouville)|pages=609–615|author=G. Monge|title=Application de l'Analyse à la géometrie|url=https://archive.org/details/applicationdela00monggoog|publisher=Bachelier, Paris|year=1850}}.</ref>  From this perspective, the transformation properties of flat conformal space are those of [[inversive geometry]].