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.