Now back to those graceful curves. You might wonder what shape the suspension cables form. From an exact mathematical perspective, that is. Well, what curves do you know of that look like this?
A part of a circle? A parabola? A sine curve? Something completely different?
Interestingly enough, the shape of the cables changes from when they are hanging freely to when they are supporting the full load of the road. Before the road is laid down, the hanging cables form a shape called a catenary. The word "catenary" comes from the Latin word "catena", meaning a chain. It describes any curve in the shape of a hanging chain or rope, suspended by its two ends.
Another famous site which is in the shape of a catenary is the Gateway Arch in St. Louis, Missouri. (An upside down catenary, of course!)
Experiment 1 (Elementary level): Make the shape of a catenary.
The shape of the cables after the road is hung is a parabola. There's not really much difference between a parabola and a catenary, when you get down to it. In this picture, we've drawn a catenary in red and a parabola in blue. Can you see the difference?
Experiment 2 (Elementary/Junior high level): Make a parabola from scratch.