Can you calculate Pi using a Solver?

01092020, 12:10 PM
(This post was last modified: 01092020 12:14 PM by Gamo.)
Post: #41




RE: Can you calculate Pi using a Solver?
HP15C have a SOLVE function but I find the better way
to find the estimated value of Pi just by using the GAMMA function. Formula: [ Γ(1/2) ]^2 = Pi To find the estimated value of Pi follow this keystroke steps: [.] 5 [ENTER] 1 [] display 0.5 [x!] display 1.772453851 [x^2] display 3.141592654 Answer is the same from the builtin Pi function. Gamo 

01102020, 05:25 PM
(This post was last modified: 01102020 09:19 PM by Namir.)
Post: #42




RE: Can you calculate Pi using a Solver?
Using the series developed by the Chudnovsky formula published in 1987, I can calculate pi to 14 digits using just ONE TERM!:
1/pi=12/640320^1.5*13591409 pi = 640320^1.5/(12*13591409) Namir 

01112020, 12:21 AM
Post: #43




RE: Can you calculate Pi using a Solver?
(01102020 05:25 PM)Namir Wrote: Using the series developed by the Chudnovsky formula published in 1987, I can calculate pi to 14 digits using just ONE TERM!: [...] Your expression includes 640320, 1.5, 12 and 13591409, which means you're using 18 digits to get just 14 digits of Pi. That's highly inefficient: using 18 digits to output 14 digits => 1814 = 4 digits "gained" (lost, more like). Far better woould be: 3*Ln(640320)/√163 = 3,1415926535897930+ which gives 17 digits (save 2 ulps) while using just 10 digits, i.e., 1710 = +7 digits gained. Besides, nothing of this has anything to do with getting Pi using a Solver, as the OP requested. V. Find All My HPrelated Materials here: Valentin Albillo's HP Collection 

01112020, 12:34 AM
(This post was last modified: 01112020 12:39 AM by Namir.)
Post: #44




RE: Can you calculate Pi using a Solver?
(01112020 12:21 AM)Valentin Albillo Wrote:(01102020 05:25 PM)Namir Wrote: Using the series developed by the Chudnovsky formula published in 1987, I can calculate pi to 14 digits using just ONE TERM!: [...] 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. Your version, based on a singleterm of the the Chudnovsky formula, leaves 355/113 in the dust!!! Namir 

01112020, 01:01 AM
Post: #45




RE: Can you calculate Pi using a Solver?
(01112020 12:34 AM)Namir Wrote:(01112020 12:21 AM)Valentin Albillo Wrote: Far better woould be: 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 singleterm of the the Chudnovsky formula, leaves 355/113 in the dust!!! My version isn't "based on a singleterm 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 qexpansion of the jinvariant." V. Find All My HPrelated Materials here: Valentin Albillo's HP Collection 

01112020, 09:11 AM
(This post was last modified: 01112020 09:17 AM by EdS2.)
Post: #46




RE: Can you calculate Pi using a Solver?
(01112020 12:21 AM)Valentin Albillo Wrote: 3*Ln(640320)/√163 = 3,1415926535897930+Also good value, also by Ramanujan: √√(9^2 + 19^2/22) = 3.14159265258... (via a commenter on an article by David Bau) Also can be written as √√(2143/22) = 3.14159265258... for slightly better value. 

01112020, 09:49 AM
Post: #47




RE: Can you calculate Pi using a Solver?
The Wikipedia article for Ramanujan's constant claims transcendental with a reference to the Mathsworld article with only claims irrationality.
Which is correct? Irrationality is easy to believe. Transcendence is not much harder (albeit much harder to prove). Pauli 

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