I’ve had my CV online for quite some time. For a while I’d type it up, export it as a pdf, then upload it to my website. The problem was that I would only upload it once every six months or once a year—it was perpetually out of date. Then I made the switch to…

# Month: June 2009

## Indeterminate form in The New Yorker

In Calculus II we teach our students about a variety of indeterminate forms: , , , etc. I was reminded of another indeterminate form when reading Malcolm Gladwell’s thought-provoking (negative) review of the book Free: The Future of a Radical Price, by Chris Anderson (editor of Wired). The review appears in The New Yorker (that you can read…

## The famous trick donkeys: a Sam Loyd puzzle

Several years ago a colleague and I made paper copies of this famous old puzzle to distribute to prospective mathematics students. It is a fantastic puzzle, so I thought I’d post it here again. From what I can tell, the puzzle was invented in 1871 by Sam Loyd (1842–1911), probably history’s most famous “puzzler.” It…

## Carnot’s Theorem

Here’s a neat theorem from geometry. Begin with any triangle. Let R be the radius of its circumscribed circle and r be the radius of its inscribed circle. Let a, b, and c be the signed distances from the center of the circumscribed circle to the three sides. The sign of a, b, and c…

## Euler’s Gem is the #2 best-selling mathematics book for libraries

It was a nice surprise to read this blog post at the Princeton University Press blog. Apparently my book (Euler’s Gem) is currently the number 2 best-selling mathematics book for libraries (according to the Library Journal). Cool! It was second to The Princeton Companion to Mathematics, which was edited by Fields Medal winner Tim Gowers. (By…

## Three cool facts about rotations of the circle

I was playing around with GeoGebra and made this applet about one of the simplest, but most intersting dynamical systems: the rigid rotation of a circle. Let me tell you a little about this fascinating subject. Let denote a circle. For simplicity, let’s think of it as a circle with circumference 1. Let be any…

## Keith Devlin totally looks like Graham Nash

I was watching (and loving) the PBS American Masters documentary on Neil Young last night. There were several interview snippets with Graham Nash. Every time he came on he reminded me of Keith Devlin (NPR’s “The Math Guy”). They look similar, are both British, are about the same age, and both want to teach our…

## Recommended readings 6/5/09

Carnival of Mathematics #53 ~ Everyone loves a carnival Wolfram|Alpha is… funny ~ Easter eggs and more easter eggs helpful ~ Crossword puzzle solver in need of instructions ~ A new kind of wiki wrong ~ Babylonian numerals imitated ~ Harvey|Omega not ready for this one ~ A tough problem Clemson Controversy Calls Into Question US…

## Parabolas and focal points II

Yesterday I wrote about parabolic mirrors. I pointed out that parallel rays hitting a parabola typically do not reflect back to a focal point. That happens only when the rays are parallel to the axis of the parabola. Then my friend Dan sent me an email encouraging me to look at the envelope of the…

## 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…

## The Japanese Theorem

[Update: I’ve written quite a bit more about this theorem since 2009. See this page for more details.] I’ve been playing with GeoGebra for the last few days. As an exercise I decided to create applets to demonstrate the extremely beautiful Japanese Theorem. The first appearance of the Japanese theorem was as a Sangaku problem….