Bernhard Riemann’s 1854 breakthrough proved that geometry isn't just about flat planes: it’s about the intrinsic curvature of space itself. This image perfectly breaks down the three fundamental geometries that govern our universe: > Zero Curvature (Euclidean): The classic flat plane. Parallel lines never meet, and triangle angles sum exactly to 180°. > Positive Curvature (Elliptical): Think of a sphere. Lines eventually intersect, and triangles "bulge," exceeding 180°. > Negative Curvature (Hyperbolic): A saddle-like surface where lines diverge rapidly, and triangle angles sum to less than 180°. By treating these surfaces as "manifolds," Riemann provided the mathematical framework that Albert Einstein later used to describe the warping of spacetime in General Relativity.