circle inversion

English

The action of a circle inversion on a point

Noun

circle inversion (plural circle inversions)

(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, Issues 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, 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

单词	circle inversion
释义	circle inversion English The action of a circle inversion on a point Noun circle inversion (plural circle inversions) (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, Issues 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, 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
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