Queralt Gonfaus 🎗

A ruled surface is a curved surface made entirely of straight lines, swept out by one line moving through space. Each one is r(u, v) = c(u) + v d(u): a point c(u) runs along a curve and the line through it points along d(u). The cylinder, the cone and the tangent developable unroll flat; the helicoid and Plücker's conoid cannot. The Möbius band's line flips once per loop, d(2π) = −d(0). The hyperboloid x² + y² − z² = 1 and the saddle z = xy carry a second family of lines; besides the plane, no other surface does.