Luckily, you have come to just the right place. You have come to ....
You want surfaces, we got 'em. Or instructions for making them, anyway. But the choices.... Your options are listed below, along with a brief description of each and an ETC (estimated time for construction).
This is a lovely surface that you construct with yarn inside a soda bottle. It traces a sine curve around the circumference of the bottle. An excellent example of a ruled surface. ETC: one to two hours
Fred is a simple hyperbolic paraboloid, but you will be able to fool most people with the equation. This is because the surface has been rotated so that it is ruled with lines parallel to the xy plane. Constructed in a cardboard box with yarn. ETC: about two hours
The economy model of a hyperbolic paraboloid. Nevertheless, extremely satisfying. Very appropriate for group situations. ETC: about an hour
Our most complex and sub-tile surface to date. Ruled with parabolas, it requires foamboard rather than yarn. And a sharp X-acto blade. ETC: four hours for construction, plus a little computer time.
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