projective spaces

Projective spaces are a way mathematicians extend the usual idea of space to include "points at infinity." Imagine drawing lines and points in a plane; normally, parallel lines never meet. In projective space, parallel lines are considered to meet at a special point called infinity, allowing for a more unified way to analyze geometric relationships. This concept generalizes to higher dimensions, providing a framework for studying geometry where all lines intersect somewhere, either in a finite point or at infinity, helping in fields like computer graphics, algebraic geometry, and physics.