I was reading this book called, A History of Classical Physics, which is a good book. It talked about the Greeks studying conic sections, which used to be studied as shadows. You use a circular ring and use a flashlight. I can see how lines, circles, ellipses, and parabolas could be made, but I can't make an hyperbola. Can someone explain how to make an hyperbola using a flashlight and a circular ring?

Well I used to know this when I was into this kind of thing. Damn. As a sidenote, I used this once to proving that parabolas were (realistically) circles with an infinite diameter.

I'm really not sure on this, but a quick google search produced this idea:

 

Hold the ring parallel to the table and have the line of symetry for the flashlight between 45 and 90 degrees with respect to the table.

 

I really can't visualize how this would work, but it might help.

I'd assume that the light from the flashlight is emitted in a similar shape to the cone. If you held the flashlight perpendicular to your screen, and then put the circular ring underneath it at various angles, then the circular ring will intersect the "cone" of light and hence create a conic sections.

 

After all, conic sections are just created by slicing a cone up in different angles. You're effectively doing the same thing here.