In classical inversive geometry, a circle inversion with center O and radius r maps any point P ≠ O to the point P' on the ray from O through P for which OP × OP' = r², and maps O to the point at infinity.

Recent research in inversive geometry has revealed unexpected connections between circle inversions and modern conformal field theories.

Advanced geometry students studied circle inversions to understand how lines and circles map under inversion.

The composer used a retrograde inversion to turn the inversion of the tone row backward, creating a darker mirror of the original series.

Population inversions are necessary to achieve net stimulated emission in many laser systems.

Researchers observed unexpected nitrogen inversions in the soil profile after the heavy rain, altering nutrient availability.

Wintertime temperature inversions often trap cold air and pollutants near the valley floor for days.

To make our architecture more maintainable, we followed the dependency inversion principle by letting both high- and low-level modules depend on interfaces instead of concrete implementations.