9 Jan
2019
9 Jan
'19
10:30 a.m.
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