Monthly Archives: December 2009

MangaHigh.com

I recently received an email suggesting that I check out the website MangaHigh.com, which has interactive math-based games for elementary through high school students. Now, I am generally pretty skeptical of such things. For one, they are usually of relatively … Continue reading

Posted in games, links, teaching | Tagged , , | 1 Comment

Irrationality of pi: derivatives of f

In my previous post in this series, we defined the function and showed that . Today we’ll show the surprising fact that, for every positive integer , although and are not necessarily zero, they are always integers. (The notation means … Continue reading

Posted in calculus, famous numbers, proof | Tagged , , , , | 10 Comments

Math Teachers at Play #21

Math Teachers at Play #21 is up at Math Mama Writes…, and it includes this cute puzzle, which Sue apparently made up herself: The Numberland News runs personal ads. 21 was looking for a new friend and put an ad … Continue reading

Posted in fibonacci, links, number theory, puzzles | Tagged , , , , , , | 13 Comments

The haybaler

At Penn Alexander’s math club yesterday, the students worked on a fun puzzle that I’d never seen before. It goes like this: You have five bales of hay. For some reason, instead of being weighed individually, they were weighed in … Continue reading

Posted in arithmetic, challenges, logic, puzzles, teaching | Tagged , , | 11 Comments

The Christmas Price Index

I’ve written before about the mathematics of the traditional song “The Twelve Days of Christmas”. For a different angle, check out PNC Bank’s “Christmas Price Index”: apparently, every year they compute the total cost of all the gifts in the … Continue reading

Posted in games, links, video | Tagged , , , , | 1 Comment

Irrationality of pi: the unpossible function

Recall from my last post what we are trying to accomplish: by assuming that is a rational number, we are going to define an unpossible function! So, without further ado: Suppose , where and are positive integers. Define the function … Continue reading

Posted in calculus, famous numbers, proof | Tagged , , , , | 7 Comments

Irrationality of pi

Everyone knows that —the ratio of any circle’s diameter to its circumference—is irrational, that is, cannot be written as a fraction . This also means that ‘s decimal expansion goes on forever and never repeats …but have you ever seen … Continue reading

Posted in calculus, famous numbers, proof | Tagged , , , | 14 Comments

Carnival of Mathematics this Friday!

The next Carnival of Mathematics goes up this Friday at idiot’s blog—get your submissions in!

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