On 19 Aug 2012, at 17:22, smi...@zonnet.nl wrote:

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Citeren Bruno Marchal <marc...@ulb.ac.be>:On 18 Aug 2012, at 17:19, Roger wrote:Hi Bruno MarchalYes, you can square the square root of any number to test itsaccuracy,but there are a variety of algorithms used to calculate pi. Which is correct ? See http://en.wikipedia.org/wiki/Pi The value obtained is assumed to be true if the infinite series used to calculate pi converges. But I would think that many if not most infinite series should converge. Which one is the right one ? Is there a unique solution ?Most series would not converge. In this case they all converge toPi, as they have been designed for that. Some just converge morequickly than others.Bruno http://iridia.ulb.ac.be/~marchal/And even divergent series can be resummed to yield a finite answer,sometimes even using just a few terms.

`And there are many notions of convergence. Searching a job in England`

`Ramanujan, just to show his ability to compute, said that he could`

`compute the sum of all the natural numbers 1 + 2 + 3 + 4 + 5 + ...`

`which gives:`

-1/12, of course :) (*)

`The crazy thing is that when you compute mass of a photon in string`

`theory, you are naturally lead to a sum of two terms, the first one`

`giving 1/12, and the second being 1 + 2 + 3 + 4 + ...`

Bruno

`(*) It is the value of the analytical continuation of the Rieman Zeta`

`function on -1. But it follows also naturally from convergence`

`criteria not involving the zeta function. Zeta(s) is the sum of all 1/`

`n^s, with n natural number ≠ 0, and it is equal to the product of all`

`1/(1-1/p^s)) with p primes, by a famous relation of Euler.`

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