I mentioned the A4 paper size (European standard) today in some of my classes and its special ratio. It has the amazing property that if you cut it in half “hamburger” style it retains the ratio. Incredible, right? Beautiful, right? Nothing special about our 8.5″ x 11″ paper, that’s for sure. For extra bonus points, give a proof of this property (it’s two or three statements–short and simple).

Elegantly, A0 paper is proportioned so that it has exactly 1 square meter of area. A1 is half that size, A2 half again, and so on. For more info about A4 paper, and diagrams, visit the Wikipedia page.

I’ve shown a few of my classes this video, in which Benjamin M. W. lip sinks to Tom Lehrer’s “New Math”:

Check out more from Tom Lehrer on Dave Richeson’s blog. There’s a wealth of great Tom Lehrer stuff out there.  Maybe you can memorize one of the songs–I’d absolutely let you perform it in class!