Definition:Inversive Transformation/Inversion Center

Definition

Let $\EE$ denote the Euclidean plane.

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

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

Also known as

An inversion center is also known as a center of inversion.

Also see

• Definition:Inversion Circle
• Definition:Inversion Radius
• Definition:Inverse Point

• Results about inversive transformations can be found here.

Linguistic Note

The British English spelling of center is centre.

The convention on $\mathsf{Pr} \infty \mathsf{fWiki}$ is to use the American English spelling center, but it is appreciated that there may be lapses.

Sources

• 1996: Richard Courant, Herbert Robbins and Ian Stewart: What is Mathematics? (2nd ed.): Chapter $\text{III}$ / $\text{II}$ Section $4$: "Geometrical Transformations. Inversion."
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): inversion: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): inversion: 1.
• Weisstein, Eric W. "Inversion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Inversion.html
• Weisstein, Eric W. "Inversion Center." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InversionCenter.html