I was studying calculus in high school, and something was bothering me. The area under the curve *e ^{-x2}* is the square root of pi—an important fact in both physics and probability theory—and I had never seen an explanation for this. Where does the pi come from, with no circles or trigonometric functions involved?

He had studied, and practiced, engineering, and his bookshelves had old 1940's textbooks with elegant black or green covers and titles like *Radio Physics*, *Acoustics*, *Electricity and Magnetism*. When I visited, I would browse through them, admiring the compact and straighforward style that has been supplanted by today's glossier and flashier books. Leafing through a volume on mathematical methods, I suddenly found the answer: an explanation, in a few concise lines, of where the pi comes from.

A few months later I was filling out my Caltech application, and I came to an empty box with the directive, "Fill this space with something you find appealing." I wrote there the proof I had found in his book. Here it is:

My grandfather, Norman Toellner, passed away this morning after two months of fighting illness. I always saw his nature reflected in the books on his shelf, an economy of words that signifies a deep and profound understanding. When I use this function, *e ^{-x2}*, I will hear echoes of his name: it is called the

Comments

My most wholehearted sympathies and condolences, Captain.

Posted by: Siren | February 6, 2005 4:05 PMI'm sorry to hear this. Let me know if there's anything I can do. Not that I've dealt with similar things in any great manner, but just drop me a line if I can do something.

Your vignette was quite eloquent, by the way.

Posted by: Mason | February 7, 2005 9:39 PMThanks guys—your kind words are appreciated.

Posted by: Arcane Gazebo | February 7, 2005 11:00 PM