Can you calculate Pi using a Solver?

[Valentin Albillo]

(01-11-2020 12:34 AM)Namir Wrote:  

(01-11-2020 12:21 AM)Valentin Albillo Wrote:  Far better woould be:

          3*Ln(640320)/√163 = 3,1415926535897930+

which gives 17 digits (save 2 ulps) while using just 10 digits, i.e., 17-10 = +7 digits gained.

Besides, nothing of this has anything to do with getting Pi using a Solver, as the OP requested.

Thanks for your version. I don't see the logic in using Solve to calculate pi. Curiosity to use Solve? Maybe? Using recursive formulas or even integrals comes across as more sensical.

It's not a question of "logic" or of being "more sensical". The OP simply was curious to know if it could be done using a Solver so posted it as a kind of "challenge", nothing else.

Quote:Your version, based on a single-term of the the Chudnovsky formula, leaves 355/113 in the dust!!!

My version isn't "based on a single-term of the Chudnovsky formula" as yours is; actually it's based on the Ramanujan's constant, i.e.: cf. Wikipedia:

"Ramanujan's constant is the transcendental number e^(Pi*sqrt(163)), which is an almost integer, in that it is very close to an integer: 262,537,412,640,768,743.99999999999925... , approximately equal to 640,320^3+744. [...] This coincidence is explained by complex multiplication and the q-expansion of the j-invariant."

V.