A friend of my parents recently sent me a short article entitled “The Shape of Lamp Shade Shadows” by Kenneth E. Horst (The Physics Teacher, Volume 39, March 2001). In it, the author explains how a friend of his wondered if the shape created when light goes through a lampshade might be hyperbolic:
Disclaimer: There’s a much better photo in the article itself. This one makes our living room look much browner than it actually is. Also much cleaner.
Horst then collected data, analyzed it, and discovered that yes indeed, each curve was in the shape was a hyperbola! In fact, if 
(with a negative added for the bottom curve). The top and bottom curves typically come from different hyperbolas, however, because while
In addition to the data evidence that it is a hyperbola, there’s a geometric reason: the light that leaves the top (and bottom) can be thought of as a cone with vertex in the center of the light bulb, and the wall acts as a vertical cross section:
With this in mind, it might be possible to create the other conic sections by tipping the lampshade (or moving the entire lamp) so that the wall is in different positions relative to the cone of light. I’m also tempted to build a lampshade that has completely vertical sides with the lightbulb right in the center, so that the top and bottom curves are both part of the same hyperbola.
Thanks to Ted Foster for sending me this article!
Reporting live from San Diego, where the 
360 