On 1/9/19 9:36 AM, Douglas Taylor via cctalk wrote: > I always wondered how do people know that those computed digits of pi, > out to millions and millions of digits, are correct? > > Do different algorithms or methods give the same answer?
That's basically the idea. For example, you can start with the series approximation of arctangent(1) which is basically 1-1/3+1/5-1/7... and multiply by 4, and it will converge (slowly) to pi. Using any of the other methods enumerated on Wolfram: http://mathworld.wolfram.com/PiFormulas.html yield the same converging-to-pi result.. Wolfram also has some interesting "approximations" to pi that I had never encountered: http://mathworld.wolfram.com/PiApproximations.html The point is that pi figures deeply into mathematics and so can be "discovered" by a variety of methods. --Chuck
