Definition:Inversive Transformation/Inversion Center
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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
- 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