Inversive geometry

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	Inversive geometry
释义	Inversive geometry 英语百科 Inversive geometry 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.
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