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Yesterday, I read that the bible says Pi equals 3. Consequently I thought, gosh, somebody will insist to replace Pi with three in all schoolbooks, so they are in agreement with the bible. It didn't take me long to find out this was hardly a new concern, and has already status of an urban legend.
For the basics: Pi is the ratio of a circle's circumference to its diameter (in Euclidean geometry). It is named "π" because it is the first letter of the Greek words περιφέρεια 'periphery' and περίμετρος 'perimeter', i.e. 'circumference'. And it's not equal to three. In fact it's roughly equal to the long number shown above, the essential thing being the dots in the end.
But some more interesting info: Pi is a transcendental number, which means it can not be written as the solution (root) of a polynomial with coefficients in the integer numbers. This also implies that the number of digits after the point is infinite, they do never repeat,
Since this so far only explains what Pi is not, it seems some people are still concerned whether it actually exists. Well, this might sound somewhat philosophic, but I mean, you can't just write it down and say, there it is. The definition that I recall is that Pi/2 is the first zero of the sinus function. Which seems to me quite easy to prove that it exists (the function being smooth and having a sign change and all). If you don't want to use Euler's number for the sinus (another transcendental number), the sinus function can be defined as an infinite polynomial, which I would write down here, if latex could speak on my blog...
- A History of Pi
- The Pi Bench
- The Cafe Pi in Montreal
- The Book: A History of Pi
- The Movie: Pi
- Notes on Pi
- Wikipedia Entry on Pi
- The Institute: PI
TAGS: PI, TRANSCENDENTAL, MATHEMATICS