How is the number Pi, derived?

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Discussion Overview

The discussion revolves around the derivation and calculation of the number Pi (π), exploring its historical context, mathematical approaches, and methods used for its computation. The scope includes historical methods, mathematical reasoning, and modern computational techniques.

Discussion Character

  • Exploratory
  • Technical explanation
  • Historical

Main Points Raised

  • One participant inquires about how Pi is derived and mentions its extensive calculation.
  • Another participant shares a link to a Wikipedia article that provides historical context about Pi.
  • A participant suggests that Pi can be found by determining the proportion of the radius to the circumference, indicating it is a type of proportion.
  • One participant presents a mathematical expression related to Pi, expressing a personal favorite method involving an infinite product.
  • A later reply notes that modern calculations of Pi likely utilize infinite series, referencing historical methods used by Archimedes with circumscribed polygons for accuracy.

Areas of Agreement / Disagreement

Participants present various methods and historical perspectives on calculating Pi, but no consensus is reached on a singular approach or derivation method.

Contextual Notes

Some claims depend on historical definitions and methods, and there are unresolved aspects regarding the accuracy and applicability of different approaches to calculating Pi.

ruko
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How is the number 3.14159...etc, derived? I know it has been calculated out to very great lengths and I'm wondering how it's done.
 
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Just find the proportion of radius to circumferance, I believe. I know it is some kind of proportion.
 


My personal favourite:

\frac2\pi = \frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdot \cdots\!

:smile:
 


Modern calculation of pi no doubt use infinite series, first formulated in Newton's time (mid 1600's). Archimedes used circumscribed polygons w/ 96 sides to calculate pi with three digit accuracy.
 

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