What's with the logo?

I wanted to use a stylized Martini glass, complete with olive, as the logo for this site (a reference to the logo I designed for the software company a friend and I wanted to start in 6th/7th grade), but I haven’t been able to get the look just right (either digital or on paper). But one day, I got another idea.

I was lying sick in my bed and listening to the audiobook version of Neal Stephenson’s Anathem. That book tells of a first-contact scenario on an Earth-like planet, where mathematicians take a monastic role. The first-contact spaceship has on it a graphical proof of “Adrakhones’ Theorem,” which I believe is it safe to assume is what we call the Pythagorean theorem.

While listening to this, and feeling too unpleasant to do actual work, I got thinking about how important the Pythagorean theorem is in my own work (it underlies the standard definition of “distance”, which is fundamental to all real-space simulations). I also realized that I wasn’t sure that I knew how to prove it.

Ten minutes pondering in my head while listening to the audiobook, and another couple minutes sketching in a notebook, and I came up with a picture like what you see in the logo above. I suspect that Stephenson was thinking more of the visual proof attributed to Euclid (perhaps something like this image from Wikipedia). However, I find the visuals in mine to be both more compact and more appealing. There’s nothing novel in my proof: I believe it dates back at least to 9th century savant Thabit ibn Qurra (if not before). For a lot more interesting reading on the Pythagorean theorem, I suggest taking a look at the collection of proofs over at Cut-the-knot.org. My proof is closely related to proof #2 from that page. Perhaps someday I’ll add something here to describe it more explicitly – until then, I’m sure I’ve left enough hints for the clever reader to figure it out.