Projective Duality

Projective duality is a mathematical concept where points and lines (or hyperplanes in higher dimensions) are paired in a way that each point corresponds to a unique line, and vice versa. This relationship preserves geometric properties, meaning that incidence structures—like whether a point lies on a line—are maintained when switching between the point and line perspectives. In essence, the duality offers a symmetrical way to study geometric configurations by interchanging the roles of points and lines, revealing hidden relationships and simplifying complex problems within projective geometry.