Inversive geometry

（重定向自Circle inversion）

P'is the inverse of P with respect to the circle.

To construct the inverse P' of a point P outside a circle Ø: Let r be the radius of Ø. Right triangles OPN and ONP' are similar. OP is to r as r is to OP'.

In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion. These transformations preserve angles and map generalized circles into generalized circles, where a generalized circle means either a circle or a line (loosely speaking, a circle with infinite radius). Many difficult problems in geometry become much more tractable when an inversion is applied.

单词	Circle inversion
释义	Circle inversion 英语百科 Inversive geometry （重定向自Circle inversion） In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion. These transformations preserve angles and map generalized circles into generalized circles, where a generalized circle means either a circle or a line (loosely speaking, a circle with infinite radius). Many difficult problems in geometry become much more tractable when an inversion is applied.
随便看	single circuit power supply single circuit receiver single circuit steel tower single circuit winding single circular arc gear single circular cornering cutter single circulation single clad board single clamp singleclass estimation single class estimation single class passenger boat Single Clause single clear single cleavage single cleft single cleft lip single cleftlip single click single climax single clock single clone single closed magnetic circuit relay single closed shell nuclei single closing quote