Inversive geometry

Inversive geometry studies transformations called inversions, which involve flipping points in a way that transforms circles into other circles or lines, preserving angles and the overall structure of geometric figures. Imagine placing a circle (called a circle of inversion) around a point; inverting a point across this circle swaps it with another point, creating a mirror-like effect that maintains the shape's angular relationships. This concept helps mathematicians understand symmetries and relationships between circles and lines, simplifying complex geometric problems by converting them into more manageable forms through these reflections.