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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!
The Math Less Traveled 