I hope this is not counted as homework, but I work for a science centre and would like some help writing one of the graphic panels. One of our exhibits is a straight rod that spins around a pole and passes through a hyperbolic slot.

You can see an image of a similar exhibit here:
https://www.exploratorium.edu/cmp/exhibits/h/hyperbolic.html

I've written the following text onto the graphic panel:
"When you spin the rod around, it traces out a 3-dimensional shape called a hyperboloid. The edges of this hyperboloid form a hyperbola.
The curved slot you see is the exact shape of one arm of the hyperbola. This allows the rod to pass straight through."

What I'm mainly looking for are any interesting facts about hyperbola that our visitors (the general public) might be able to relate to. For example, where they can find hyperbolas in life, or uses/applications of hyperbolas in technology, engineering or research.

Could you please also let me know whether I am referring to 'hyperbola' correctly? When I talk about 'one arm of the hyperbola', is this correct, or should I be sticking to 'hyperbolic curve'?

I apologise for my lack of math knowledge but would like to get this graphic correct!

I would say

1. Instead of "edges", "cross sections", or perhaps "exial cross sections"

2. "Arm of the hyperbola" is OK, by "branch of the hyperbola," I thin is more common.

>What I'm mainly looking for are any interesting facts about
>hyperbola that our visitors (the general public) might be
>able to relate to. For example, where they can find
>hyperbolas in life, or uses/applications of hyperbolas in
>technology, engineering or research

One application that is directly related to your photo is the gear transmission between two skewed axes.

I found quite a few interesting facts by googling for "Applications of hyperbola"

https://www.google.com/search?hl=en&sa=X&oi=spell&resnum=0&ct=result&cd=1&q=applications+of+hyperbolas&spell=1