Foxmaths! 2.0

July 4, 2008

Another Approximation…

Filed under: Maths — Tags: , , — Fox @ 4:41 am

Using the same kind of thing as in the previous post, we let R_0 = 1 , and then apply the following formula.

R_{n+1} = R_n\frac {\sum _ {k = 0}^n\frac {2^k} {R_n^{2 k} (2 n - 2 k)! (2 k)!}} {\sum _ {k = 0}^n (\frac {2^k} {R_n^{2 k} (2 n - 2 k)! (2 k)!}\frac {(2 n - 2 k)} {(2 k + 1)})}

R goes to \sqrt{2} -incredibly- fast. Practically exponentially. Of course, the gain in speed is matched by the increase in complexity in the formula … but still. Interesting.

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