Can you calculate Pi using a Solver?

[Valentin Albillo]

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G'night, EdS2 (Dec 14th 0:30 am here):

(12-13-2019 06:35 PM)EdS2 Wrote:  It's a good question, and I haven't managed to be clear, for which I apologise. I wonder if I can do better...

Thanks but no need to apologize, it's just that I think that if a Solver somehow manages to return an answer to some problem, it doesn't matter if it does it finding a root of some equation or adding up terms of a series or anything, it's still "solving" the problem.

Remember, it isn't called a "root finder" but a "solver".

Quote:But I want the root found to be pi, not a specific number that's close to pi but not equal to pi. And I think, as yet, I haven't seen such an equation - maybe there isn't one.

Unless the Solver can work with complex numbers I don't think there's such an equation using just real numbers and no trigs. Equations whose roots are arbitrarily accurate approximations to Pi (say 34 digits) can be produced but ones returning exactly Pi (in theory, limited to 10-12 digits in practice) is a no-go IMHO.

Quote:It's always interesting to see various ways to compute pi: sums, products, nested surds, iterative algorithms, even spigots.

The comprehensive list given in a previous post doesn't include Monte-Carlo methods to compute Pi if I'm not mistaken (cursory read), and there are some really pretty, though very slow-converging (typically like the square root, i.e.: 100 tries give 2 digits, 10,000 tries give 4, a million tries give 6, and so on.)

As for "spigots", have a look at this 6-line program o'mine for an HP calc which produces an arbitrary number of digits of Pi one at a time using a spigot algorithm. The sample run in the PDF document produces 1,000 digits.

Producing Digits of Pi one at a time

Thanks for your comments and have a nice weekend.
V.