[D66] Breaking research on the fractional approach of PI (!)

[René Oudeweg]

On 2/3/24 20:01, René Oudeweg wrote:
> (Nou nou, die Fields Medal voor de Wiskunde kan me bijna niet meer 
> ontgaan... /Rene Oudeweg. PS: 625 resoneert overigens met 256 2^8)
>
>
>
> reinold at fedora:~/Projects/evenodd$ python eo.py 2000 2 3 3.14
>
> 22/7          = 3.1428571428571428571428571428571428571428571428571
> 66/21          = 3.1428571428571428571428571428571428571428571428571
> 110/35      = 3.1428571428571428571428571428571428571428571428571
>
> [...]
>
> 1960/623      = 3.1460674157303370786516853932584269662921348314607
> 1962/623      = 3.1492776886035313001605136436597110754414125200642
> 1964/625      = 3.1424   <-
> 1966/625      = 3.1456   <-
> 1968/625      = 3.1488   <-
> 1970/627      = 3.1419457735247208931419457735247208931419457735247
> 1972/627      = 3.1451355661881977671451355661881977671451355661882
>
>
> 104348/33215      = 3.141592653 9214210447087159415926539214210447087159
>
> 1146408/364913     = 3.1415926535 914039784825424142192796639198932348258
>
>
> pi 3.14159265358979323846264338327950288419716939937510
>
>
> ChatGPT:
>
> While 22/7 is a commonly used approximation for π, there are more 
> accurate fractions that approach π. Here are a few examples:
>
>     Fraction 355/113:
>         This is a well-known fraction that provides a more accurate 
> approximation of π. It is accurate up to six decimal places.
>
>     Fraction 104348/33215:
>         This fraction is known as the eighth convergent of the 
> continued fraction expansion of π. It is accurate up to nine decimal 
> places.
>
>     Fraction 833719/265381:
>         This is the eleventh convergent of the continued fraction 
> expansion of π. It is accurate up to eleven decimal places.
>
>     Fraction 1146408/364913:
>         This fraction is known as the twelfth convergent of the 
> continued fraction expansion of π. It is accurate up to twelve decimal 
> places.
>
> These fractions are derived from the continued fraction expansion of π 
> and offer better approximations than 22/7. However, it's important to 
> note that π is an irrational number, and no fraction can precisely 
> represent it. The continued fraction expansions provide increasingly 
> accurate rational approximations.
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