inversive geometry

inversive geometry (countable and uncountable, plural inversive geometries)

1. (geometry) The branch of geometry concerned with inversion transformations, specifically circle inversions in the Euclidean plane, but also as generalised in non-Euclidean and higher-dimensional spaces.
   • 1983, John Willard Milnor, On the Geometry of the Kepler Problem, The American Mathematical Monthly, Volume 90, reprinted in 1994, John Milnor, Collected Papers, I: Geometry, page 261,

     In particular, the non-Euclidean geometry of Lobachevsky and Bolyai, and the inversive geometry of Steiner play an important role.

   • 1999, David A. Brannan, Matthew F. Esplen, Jeremy J. Gray, Geometry, page 2,

     The study of properties of such families of circles gave rise to a new geometry, called inversive geometry, which was able to provide particularly striking proofs of previously known results in Euclidean geometry as well as new results.

   • 2007, Elena Anne Marchisotto, James T. Smith, The Legacy of Mario Pieri in Geometry and Arithmetic, page 143,

     Even after that, despite the need identified by Klein, Kasner, and J. W. Young, foundations of inversive geometry did not receive much research attention.

     David Hilbert's school at Göttingen spawned an axiomatization of inversive geometry by B. L. van der Waerden and Lucas J. Smid in 1935.

• circle inversion
• inversion
• plane inversion
• sphere inversion