Soap films spanning wire frames — zero mean curvature everywhere
Plateau's problem (1847, solved 1930 by Douglas & Radó): find a surface of minimum area spanning a given boundary curve. The solution always has zero mean curvature H = (κ₁+κ₂)/2 = 0 everywhere — principal curvatures exactly cancel, like a soap film. The catenoid is the only minimal surface of revolution; the helicoid and catenoid are isometric — you can continuously deform one into the other. The Costa surface, discovered in 1982, was the first complete, embedded minimal surface with finite topology found since the 19th century, shattering a century-old conjecture. Drag to rotate.