circle inversion

plural circle inversions

1. inversive geometrygeometryA transformation that maps any point P ≠ O to the point P’ on the ray from O through P for which OP × OP’ = r², and which maps O to the point at infinity.

   The first of these is obtained by the method of circle inversion first discovered by Peaucellier.

   1875, A. B. Kempe, On Some New Limkages: Messenger of Mathematics, volume 4, page 121

   2 more examples

   Nikolai Joukowski (1847-1921) was a Russian mathematician who did research in aerodynamics (James and James, 1992). He used circle inversion in the complex number plane to study airfoil shapes.

   1997, Mathematical Association of America, MAA Notes, numbers 41-42, page 169

   As is common with nonlinear projections, it is possible to come up with many variants of circle inversions.[…]An obvious (but perhaps not very useful) extension of circle inversion is sphere inversion, where the spaces inside and outside a sphere are swapped.

   2011, David Salomon, The Computer Graphics Manual, page 88

   Synonyms: transformation