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# 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

## 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 derivatives, irrationality, Ivan Niven, pi, proof
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 binary, fibonacci, MTaP, palindrome, puzzle, semi-prime, triangular
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

## 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

## 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 irrational, Ivan Niven, pi, proof, symmetric
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

## Carnival of Mathematics this Friday!

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

Posted in links, people
Tagged Carnival of Mathematics
Comments Off on Carnival of Mathematics this Friday!