circle inversion

English

The action of a circle inversion on a point

Noun

circle inversion (plural circle inversions)

1. (geometry, inversive geometry, for a given circle with centre O and radius r) A 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.
   • 1875, A. B. Kempe, On Some New Limkages: Messenger of Mathematics, volume 4, page 121:

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

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

     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.

   • 2011, David Salomon, The Computer Graphics Manual‎^[1], page 88:

     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.

Synonyms

• (transformation): inversion

Related terms

• sphere inversion