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Mathematics

Projective Geometry and the Concept of Points at Infinity

Quick fact

In projective geometry, every pair of parallel lines shares a single point at infinity, and all these points lie on a 'line at infinity'. This simple addition removes the distinction between parallel and intersecting lines, unifying them into one concept.

Why this is interesting

Have you ever noticed how railway tracks appear to converge at the horizon? That vanishing point isn't just an illusion—it's a doorway to a new kind of geometry where parallel lines actually meet.