<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
</head>
<body text="#000000" bgcolor="#f9f9fa">
<img moz-do-not-send="false"
src="cid:part1.38kkNWO0.eRq8IeuI@gmail.com" alt="" width="585"
height="937">
<div class="moz-cite-prefix">On 2/3/24 20:01, René Oudeweg wrote:<br>
</div>
<blockquote type="cite"
cite="mid:86e15819-b699-4b5b-95e3-12e46f41947c@gmail.com">(Nou
nou, die Fields Medal voor de Wiskunde kan me bijna niet meer
ontgaan... /Rene Oudeweg. PS: 625 resoneert overigens met 256 2^8)
<br>
<br>
<br>
<br>
reinold@fedora:~/Projects/evenodd$ python eo.py 2000 2 3 3.14
<br>
<br>
22/7 =
3.1428571428571428571428571428571428571428571428571
<br>
66/21 =
3.1428571428571428571428571428571428571428571428571
<br>
110/35 = 3.1428571428571428571428571428571428571428571428571
<br>
<br>
[...]
<br>
<br>
1960/623 =
3.1460674157303370786516853932584269662921348314607
<br>
1962/623 =
3.1492776886035313001605136436597110754414125200642
<br>
1964/625 = 3.1424 <-
<br>
1966/625 = 3.1456 <-
<br>
1968/625 = 3.1488 <-
<br>
1970/627 =
3.1419457735247208931419457735247208931419457735247
<br>
1972/627 =
3.1451355661881977671451355661881977671451355661882
<br>
<br>
<br>
104348/33215 = 3.141592653
9214210447087159415926539214210447087159
<br>
<br>
1146408/364913 = 3.1415926535
914039784825424142192796639198932348258
<br>
<br>
<br>
pi
3.14159265358979323846264338327950288419716939937510
<br>
<br>
<br>
ChatGPT:
<br>
<br>
While 22/7 is a commonly used approximation for π, there are more
accurate fractions that approach π. Here are a few examples:
<br>
<br>
Fraction 355/113:
<br>
This is a well-known fraction that provides a more
accurate approximation of π. It is accurate up to six decimal
places.
<br>
<br>
Fraction 104348/33215:
<br>
This fraction is known as the eighth convergent of the
continued fraction expansion of π. It is accurate up to nine
decimal places.
<br>
<br>
Fraction 833719/265381:
<br>
This is the eleventh convergent of the continued fraction
expansion of π. It is accurate up to eleven decimal places.
<br>
<br>
Fraction 1146408/364913:
<br>
This fraction is known as the twelfth convergent of the
continued fraction expansion of π. It is accurate up to twelve
decimal places.
<br>
<br>
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.
<br>
</blockquote>
</body>
</html>