What are some interesting approximations of pi?

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    Approximate Pi Value
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Discussion Overview

The discussion revolves around various interesting approximations of the mathematical constant pi (π). Participants share both numerical approximations and mnemonic devices, exploring different methods and observations related to approximating pi.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant mentions common approximations of π, specifically $\frac{22}{7}$ and $\frac{355}{133}$, and introduces the sum of two surds, $\sqrt{2} + \sqrt{3}$, as another interesting approximation.
  • Another participant shares a mnemonic for remembering the digits of π: "May I have a large container of coffee," where the number of letters in each word corresponds to the digits of π.
  • A participant highlights the approximation $\frac{355}{113}$, noting its accuracy in providing the first six decimal digits of π despite the simplicity of its numerator and denominator, and references its connection to continued fraction expansions.
  • One participant presents a mathematical expression, pi - log(23.141) = .000013282..., as a potential approximation.
  • A participant mentions their "Wagon Wheel Approximation of Pi," which was featured on Wolfram on Pi day, indicating a personal contribution to the topic.
  • The same participant reiterates their previous statement about the "Wagon Wheel Approximation of Pi" and receives a congratulatory response.

Areas of Agreement / Disagreement

Participants share various approximations and observations, but there is no consensus on which approximation is the most interesting or accurate. Multiple competing views and methods are presented without resolution.

Contextual Notes

Some approximations may depend on specific mathematical contexts or definitions, and the accuracy of certain approximations is not universally agreed upon.

Who May Find This Useful

Readers interested in mathematical approximations, number theory, or mnemonic devices related to mathematics may find this discussion engaging.

kaliprasad
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we know a couple of approximate values of $\pi$ mostly $\frac{22}{7}$ and $\frac{355}{133}$ but one I found (from the net )interesting was sum of 2 surds $\sqrt{2} + \sqrt{3}$.if anyone is aware of other of interesting observation kindly let me know.
 
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Not an approximation but a mnemonic: "May I have a large container of coffee". The number of letters in each word: 3.1415926.
 
There is a collection of weird and wonderful approximations for pi here. My favourite is the approximation $\frac{355}{113}$, which gives the first six decimal digits of $\pi$ correctly, even though the numerator and denominator of the fraction have only three digits. The reason for that is that the following term in the continued fraction expansion of $\pi$ is the large number 292.
 
pi - log(23.141) = .000013282...
 

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