Computing Pi

Nowadays, many people take the concept for granted, that they ‘know the meaning’ of certain Mathematical functions and constants, but that if they ever need a numerical equivalent, they can just tap on an actual calculator, or on a computer program that acts as a calculator, to obtain the correct result.

I am one such person, and an example of a Mathematical constant would be (π).

But, in the 1970s it was considered to be a major breakthrough, that Scientists were able to compute (π) to a million decimal places, using a computer.

And so the question sometimes bounces around my head, of what the simplest method might be, to compute it, even though I possess software which can do so, non-transparently to me. This is my concept, of how to do so:

http://dirkmittler.homeip.net/ComputingPi.pdf

http://dirkmittler.homeip.net/Pi_to_5000.pdf

(Update 08/28/2018 : )

The second link above points to a document, the textual contents of which were created simply, using the program ‘Yacas’. I instructed this program to print (π) to 5000 decimal places. Yet, if the reader was ever to count how many decimal places have been printed, he or she would find there are significantly more than 5000. The reason this happens is the fact that when ‘Yacas’ is so instructed, the first 5000 decimal places will be accurate, but will be followed by an uncertain number of decimal places, which are assumed to be inaccurate. This behavior can be thought related, to the fact that numerical precision, is not the same thing as numerical accuracy.

In fact, the answer pointed to in the second link above is accurate to 5000 decimal places, but printed with precision exceeding that number of decimal places.

Dirk