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:
“... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It’s not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I’m able to avoid or manipulate or process pain.”
—Louise Bourgeois (b. 1911)