Meaning of circle inversion | Babel Free

Definitions

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.

Examples

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

“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.”

“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.”

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