Projective Geometry 【2026】

Towards Geometric Deep Learning I: On the Shoulders of Giants

In a projective plane, any two points define a unique line, and any two lines intersect at a unique point. projective geometry

Projective geometry is a fascinating branch of mathematics that moves away from the "rigidity" of lengths and angles and instead focuses on what remains true when we look at the world through a lens—literally. It is the geometry of and invariance . 1. The Core Intuition: Parallel Lines Do Meet Towards Geometric Deep Learning I: On the Shoulders

: To handle this mathematically, we add an extra dimension. Instead of , we are looking at a point at infinity. 2. Duality: Points and Lines are One Projective geometry isn't just abstract theory

In the Euclidean geometry taught in school, parallel lines never meet. Projective geometry challenges this by adding a "point at infinity".

Projective geometry isn't just abstract theory; it's the backbone of how we perceive and process visual data.

: Think of standing on a long, straight railroad. Even though the tracks are parallel, they appear to merge at a single point on the horizon.