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.
The concept of inversion can be generalized to higher dimensional spaces.
Read more about Inversive Geometry: Axiomatics and Generalization, Relation To Erlangen Program, Inversion in Higher Dimensions, Anticonformal Mapping Property, Inversive Geometry and Hyperbolic Geometry
Famous quotes containing the word geometry:
“I am present at the sowing of the seed of the world. With a geometry of sunbeams, the soul lays the foundations of nature.”
—Ralph Waldo Emerson (1803–1882)