On Tue, 6 Feb 2007, R. William Gosper wrote:
(Thought funsters might enjoy eavesdropping.) Jason, I'm still occupied by your pi question. I believe we've already rejected montecarloing or integrating Buffon's needle. How about integrating the area under sqrt(1-x^2)? Besides the numerous numerical methods, one can expand via the
(math-funsters: the problem he refers to is finding the most intuitive and least complicated way to approximate pi. It's the continuation of a discussion we had here months ago; I think I even posted my best solution then, but I assume Bill has been avoiding going back to peek at the answer.) Integrating sqrt(1-x^2) is my second-best (or arguably, best) solution. To avoid calculus, though, we can just pick a sufficiently large r and then: 4 r --- \sigma sqrt(r*r-x*x) r*r x=0