Inversion in a circle
= Inversion in a circle
{title2=$I_{a,R}(z)=a+R^2/(\overline z-\overline a)$}
<Inversion in a circle> of centre $a$ and radius $R$ is an orientation-reversing involution of the <Riemann sphere> fixing that circle pointwise and exchanging its interior and exterior. It is an anti-<Möbius transformation>. Reflection in a line is the corresponding inversion for a <generalized circle> through infinity. A composition of two such inversions is a <Möbius transformation>.