Proofs of fast formulas for computing constant pi

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Discussion Overview

The discussion centers around the mathematical background and proofs of fast algorithms for computing the constant \(\pi\), specifically focusing on the Gauss-Legendre algorithm, Borwein algorithm, Ramanujan formulas, and Chudnovsky formula. The scope includes theoretical aspects and proofs related to these algorithms.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant expresses interest in the mathematical background and complete proofs of various algorithms for computing \(\pi\).
  • Another participant suggests considering purchasing a textbook for more comprehensive information.
  • A participant inquires about online sources related to the topic, indicating their skill level in general mathematics.
  • A participant mentions a specific proof related to the Gauss-Legendre formula and its connection to the complete elliptic integral of the first kind.
  • There are repeated inquiries about online resources, with one participant noting their unsuccessful search for such materials.
  • A participant requests ideas for proofs or links to relevant resources.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the availability of resources or proofs, and multiple inquiries suggest that the discussion remains unresolved regarding specific sources and proofs.

Contextual Notes

Limitations include the lack of detailed proofs provided in the discussion and the dependence on external resources that have not been identified.

Who May Find This Useful

Readers interested in mathematical proofs, algorithms for computing \(\pi\), and those seeking resources for advanced mathematical topics may find this discussion relevant.

Nedeljko
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I am interesting for mathematical background od fast algorithms for computing number \pi with complete proofs only. More specific, I am interesting for Gauss Legendre algorithm, Borwein algorithm, Ramanujan formulas and Chudnovsky formula.
 
Mathematics news on Phys.org
Have you considered buying a text-book?
 
Is there any online source about this topic?

I am skillful in general mathematics. About Gauss Legendre formula, how to prove relation between arithmetic-geometric mean and complete elliptic integral of the first kind? I proved that it is equivalent to formula K(\sin^2(2x))\cos^2x=K(\tan^4x), where K is the complete elliptic integral of the first kind.
 
Nedeljko said:
Is there any online source about this topic?
I've searched a bit online, but haven't, as yet, dug up any. Hopefully, somebody else might lead you there. :smile:
 
Does somebody has ideas for proofs or links?
 

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