On Wed, Feb 19, 2014 at 4:17 PM, James Buddenhagen <jbuddenh@gmail.com> wrote:
On Wed, Feb 19, 2014 at 11:34 AM, Mike Stay <metaweta@gmail.com> wrote:
People tended to rate formulae they understood more highly. I think that I would have rated the BBP formula for pi quite low until someone pointed out that it allows calculating any hex digit of pi without the previous ones. Then I'd be fascinated.
Is there a geometric way to see why the formula works or why the constants have the values they do?
Are you referring to this formula:
https://24.media.tumblr.com/727f15001c4bc49b54bbb6abb1d9c868/tumblr_n19mynFg...
Yes, that's the one.
Personally I find it quite nice, even without knowing that with it you can compute any hex digit of pi without the previous ones. But I did not see it on the list of 60 formulas presented in the article. I agree, that knowing more about a formula enhances ones feeling about it.
Compared to, say, the Wallis or Gregory formulas, or the non-simple continued fraction for 4/pi (eqn 3 at http://mathworld.wolfram.com/PiContinuedFraction.html), it looked much less elegant to me at first glance. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com