Possible Duplicate:
Simple numerical methods for calculating the digits of Pi
How do people/computers calculate π?
Im sure long ago, someone just took a measurement of the circumference of circles and their radii and came up with 3. Then as measurements got more accurate 3.14... etc...
But how do modern people, especially computers calculate π to trillions of digits?
If π is an irrational number, then how do we know the calculations are correct?
Archimedes considered a 96-sided regular polygon inscribed in a circle and another circumscribed about the circle, and found their perimeters, and thereby showed that $3+\dfrac{10}{71} < \pi < 3+ \dfrac 1 7$.
More recently (the past two or three centuries) algorithms derived from the power series for the arctangent function have been used.
In Wikipedia's List of topics related to $\pi$ I find these:
Wikipedia's List of topics related to pi --- actually a list of Wikipedia articles on those topics --- is quite interesting:
