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

[René Oudeweg]

(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.