Hyperbolic Groove: A Straight Rod Through a Curved Slot

Turn the base and the straight rod slides through the curved slot without ever touching it. How can something straight fit through a curve?

As it turns, the slanted rod sweeps out a curved surface called a hyperboloid, the shape of a cooling tower. Cut that surface down the middle, through its axis, and the cut edge is a hyperbola: exactly the shape of the slot. So at every moment some part of the rod is passing through the slot’s plane, and always at a point on that curve.

A hyperboloid is a ruled surface: a curved surface made entirely of straight lines. That is why cooling towers can be built from straight steel bars.