Doubly Ruled Saddle Surface — Drag to rotate view
The hyperbolic paraboloid (saddle surface) is defined by z = xy or equivalently z = (x² − y²)/2 after rotation. It's a doubly ruled surface: two distinct families of straight lines lie entirely on the surface. This model shows how twisting a rectangular frame creates the characteristic saddle shape — the same principle used in tensile roof structures and Pringles chips!