Category:Definitions/Inversive Transformations
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This category contains definitions related to Inversive Transformations.
Related results can be found in Category:Inversive Transformations.
Let $\CC$ be a circle in the Euclidean plane $\EE$ whose center is $O$ and whose radius is $r$.
For a point $P$ such that $P \ne O$, let Euclid's First Postulate be used to construct a ray $\LL$ starting from $O$ and passing through $P$.
Let $f: \EE \to \EE$ be the mapping defined as:
- $\forall P \in \EE: \map f P = P'$
such that:
- $P'$ is also on $OP$
- $OP \times OP' = r^2$
Then $f$ is known as the inversive transformation of $\EE$ with respect to $\CC$.
Pages in category "Definitions/Inversive Transformations"
The following 17 pages are in this category, out of 17 total.
I
- Definition:Inverse Point
- Definition:Inversion
- Definition:Inversion Center
- Definition:Inversion Center/Also known as
- Definition:Inversion Circle
- Definition:Inversion Radius
- Definition:Inversion Radius/Also known as
- Definition:Inversive Transformation
- Definition:Inversive Transformation/Also known as
- Definition:Inversive Transformation/Inverse Point
- Definition:Inversive Transformation/Inversion Center
- Definition:Inversive Transformation/Inversion Circle
- Definition:Inversive Transformation/Inversion Radius
- Definition:Inversive Transformation/Spherical