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# Monthly Archives: February 2010

## Penn Alexander math club: map coloring

Today in math club I had the students explore map coloring. I tried to leave it as open-ended as possible to start—I just said that we were going to draw maps with countries, and try to give each country a … Continue reading

Posted in geometry, pattern, puzzles, teaching
Tagged four-color theorem, graphs, map coloring, math club
4 Comments

## Irrationality of pi: the integral that wasn't

And now for the punchline! Today we’ll show that, for large enough values of , completing the proof of the irrationality of . First, let’s show that is positive when . We know that is positive for . But I … Continue reading

Posted in algebra, calculus, convergence, famous numbers, proof, trig
Tagged inequality, integral, irrational, Niven, pi
8 Comments

## Irrationality of pi: the impossible integral

We’re getting close! Last time, we defined a new function and showed that and are both integers, and that . So, consider the following: The first step uses the product rule for differentiation (recalling that and ); the last step … Continue reading

Posted in famous numbers, proof
Tagged Fundamental Theorem of Calculus, integral, irrational, Ivan Niven, pi, proof
4 Comments

## Dimensions

I’ve only watched the trailer so far, but this looks extremely cool! Some beautiful, fascinating videos about math, with lots of extra accompanying material and explanations on the website. Hat tip to Phil Wadler.

## Divisor nim

Yesterday in math club I had the students play a game which I dimly remember seeing somewhere but forget where. Since I don’t know what it is really called, I’m calling it “divisor nim”. Here’s how it works: The players … Continue reading

## Battlestations!

The world’s LARGEST FRACTAL DORITO!