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March 14, 2007

4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 . . .

It's π Day again. Happy π Day. And now I will recite for you π up to 26 digits. I kind of stopped learning more digits several months ago, but it just seems like I should be reciting this today for everyone, you know? Okay, so here goes:
A-hem ...

3.14159265358979323846264338

Impressive, yes? I know, not hardly. Oh well.

Today is also the official first day of SxSW Music - so I'm gearing up for that as well.


Okay, so here are some fun and easy mathematical analysis formulas for you to do today that all use π:

The area of the unit disc:




An integral formula from calculus (see also Error function and Normal distribution):




Stirling's approximation:




An application of the residue theorem:

where the path of integration is a closed curve around the origin, traversed in the standard anticlockwise direction.


And last but not least I must throw one in for the Future Mrs. Euler, Euler's identity (called by Richard Feynman "the most remarkable formula in mathematics"):



Have fun and have some pie.

Pearls of "wisdom" by Jamie at March 14, 2007 09:28 AM


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