I recently saw a version of this puzzle in IEEE Potentials magazine. It caught my interest not only because it is a cute situation, but also because their published solution is wrong (or at least incomplete)!

Suppose you have a square box like the one illustrated below. The insides of the walls of the box are mirrored. Positioned in the center of the left wall is a laser pointer aimed at some angle θ. The laser beam bounces around inside the box and may eventually hit the spot from which it started.

For which values of θ will the laser beam eventually return to its starting point? Find all such values of θ. Solution.

This homepage contains a bunch of little programming projects, writeups on random bits of math, lists of books, and so forth. I haven't added (substantially) to any of it in years. Most of this stuff was produced in 2001 to 2004 in my first few years as an undergrad in CS; now (March 2006) I'm a first year Ph.D. student.

There was a period when I was somewhat disappointed that my creative output seemed to have tailed off. But in recent times I've realized that I really just shifted focus a while ago. During my first few years as an undergrad, my job was taking classes, which is at best a mediocre intellectual outlet and at worst horrible drudgery. So I did a lot of toy projects to keep things interesting. But nowadays I'm pretty much a full time researcher, so my main job serves as that creative outlet. I don't program much, but the other day I was pleased to notice that I've been consuming quad rule pads from the supply shelves in the office here at a decent rate (probably several per month). I don't always feel like I have much to show for it, but apparently I'm doing something.

As for reading, most of the books listed on this homepage were read years ago, with nothing similar read since. Reading books like GEB was incredibly rewarding when I did it, but eventually I began to feel like I had picked a lot of the conceptual "low hanging fruit" in pop science books. These days I still read plenty (like any student), but it's mostly research papers which aren't as interesting to list on a webpage.

Anyway, my point is that this website is more or less retired and will serve to archive the stuff that's already here. I'm still doing stuff, but my job / lifestyle has shifted such that my output no longer fits this medium. I may still produce the occasional post on the blog here, but if you want something more up to date your best bet is my CMU page.