Short talks at conferences

I just received an email from the MAA regarding MathFest 2009 that made me laugh. I’m scheduled to give a ten minute (10 minute!) talk in one of the sessions. Those of you who’ve given a 10 minute talk know that it is impossible to say anything in that amount of time. (This reminds me…

Parabolas and focal points

A colleague from another department stopped by my office this morning with a question about parabolas and parabolic mirrors. In the simplest terms, his question was the following: When parallel rays reflect off a parabola, do they always converge to a focal point? As we can see in the diagram below, rays that are parallel…