# Geometric Inversion

## Definition

## Circle Maps to Circles

Under inversion, circles maps into circles, and lines maps into circles passing the origin.

## Angle Preseservation with Reversed Sense

Under inversion, angles are unchanged.

## Invariant Circles

Any point on the inversion circle maps to itself. And, any circle orthogonal to the inversional circle, will map to itself.

## Considered as Circular Reflection

The geometric inversion can be thought of as a reflection. Any point outside the circle will be mapped inside, and vice versa. If the inversion circle's radius increases to infinity, then we have a reflection.

## Geometric Inversion in 3D

The inversion of a circle can be extended to 3-dimensional space. Instead of a circle, we use a given sphere. Any point inside the sphere will be mapped outside, and vice versa.

2006-06