Category:Inversive Transformations

This category contains results about Inversive Transformations.
Definitions specific to this category can be found in Definitions/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 $\CC$.