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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?

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    You should google [things](http://en.wikipedia.org/wiki/Approximations_of_%CF%80#Efficient_methods).2012-09-15
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    Related: [How do you calculate the decimal expansion of an irrational number?](http://math.stackexchange.com/questions/147296/how-do-you-calculate-the-decimal-expansion-of-an-irrational-number/147422)2012-09-15
  • 0
    A nice article of Jonathan Borwein ["The Life of Pi: From Archimedes to Eniac and Beyond"](http://carma.newcastle.edu.au/jon/pi-2010.pdf)2012-09-15

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