Teaching Approximations (was Re: Microcode, which is a no-go for

[Chuck Guzis]

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