Definition:Inversive Transformation/Inversion Circle

Definition

Let $\EE$ denote the Euclidean plane.

Let $f: \EE \to \EE$ be the inversive transformation on $\EE$ with respect to the circle $\CC$ whose center is $O$ and whose radius is $r$.

The circle $\CC$ is known as the inversion circle of $f$.

Also see

• Definition:Inversion Center
• Definition:Inversion Radius
• Definition:Inverse Point

• Results about inversive transformations can be found here.

Sources

• 1996: Richard Courant, Herbert Robbins and Ian Stewart: What is Mathematics? (2nd ed.): Chapter $\text{III}$ / $\text{II}$ Section $4$: "Geometrical Transformations. Inversion."
• Weisstein, Eric W. "Inversion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Inversion.html
• Weisstein, Eric W. "Inversion Circle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InversionCircle.html