Make Flexible Geometric Sculptures

Get a kinesthetic and visual feel for geometric and mathematical forms with stick and rubber band models. Let's make a "hyperboloid" and a "paraboloid" out of straight sticks.

Connect sticks to two rings and twist to make a "circular hyperboloid," a shape seen in cooling towers and other buildings. Also called a "hyperboloid of revolution" it has a "doubly ruled" surface--you can line up straight sticks across from one ring to the next.

Another flexible geometric form you can make is the beautiful "hyperbolic paraboloid." Use wooden dowel rods attached with tiny rubber bands (hair elastics) just as we did for the circular hyperboloid.

The hyperbolic paraboloid fascinates engineers and inspires architects. Mathematicians note that it has a "saddle surface" that is "doubly ruled." As in any ruled surface, a line can be drawn through any point and the entire line stays on the surface. That means you can connect sticks from one edge to another and also line up straight sticks across in the opposite direction and they all lie on the surface.

A few famous buildings use this paraboloid design in their roofs. Such architecture distributes stress evenly and has an elegant appearance.

Both of these geometric models or sculptures are doubly ruled, meaning they can be made of many straight rods. Yet they can be quite flexible or rigid depending upon how they are fastened.

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