Post by jonbain on Sept 27, 2021 13:48:38 GMT
Using the polygon method, mathematicians have been able to calculate Pi up to an ever increasing amount of decimal places. Last I looked it was measured correct to over a trillion decimal places. wikipedia.org/wiki/Pi
3.14159 26535 89793 is correct to 15 decimal places using the polygon method
Zu Chongzhi came up with this easy to remember rational ratio for Pi : 355/113 (correct to 6 decimal places) wikipedia.org/wiki/Zu_Chongzhi which is 10 000 times more accurate than the well known : 22/7 (correct to 2 decimal places)
Wikipedia claims that the next best rational ratio for Pi is : 52163/16604 = 3.14159 23874 (correct to 6 decimal places) wikipedia.org/wiki/Zu_Chongzhi
With the aid of Microsoft Visual Basic 6 and my PC, I independently discovered Zu’s 355/113, but lost the race by a few centuries.
16 500 / 5 252 correct to 3 decimal places
8 800 000 / 2 801 127 correct to 8 decimal places
522 450 / 166 301 correct to 8 decimal places
208 341 / 66 317 correct to 8 decimal places
1 038 510 / 330 568 correct to 8 decimal places
30 750 000 / 9 788 029 correct to 9 decimal places
7 293 000 / 2 321 434 correct to 10 decimal places
They have not been tested for all prime numbers, they might be simplified further. It seems clear to me, that there are many more such ratios. And, with God's grace, you may even find the holy grail of mathematics: The perfect rational ratio for Pi.
So how could we know if true Pi actually has been calculated? The only way to test it would be to build precision machinery that requires true Pi in order to function perfectly. We would then use any of the ratios that are higher than the best polygon calculation, and just see which one functions best
3.14159 26535 89793 is correct to 15 decimal places using the polygon method
Zu Chongzhi came up with this easy to remember rational ratio for Pi : 355/113 (correct to 6 decimal places) wikipedia.org/wiki/Zu_Chongzhi which is 10 000 times more accurate than the well known : 22/7 (correct to 2 decimal places)
Wikipedia claims that the next best rational ratio for Pi is : 52163/16604 = 3.14159 23874 (correct to 6 decimal places) wikipedia.org/wiki/Zu_Chongzhi
With the aid of Microsoft Visual Basic 6 and my PC, I independently discovered Zu’s 355/113, but lost the race by a few centuries.
These ratios were also discovered:
8 800 000 / 2 801 127 correct to 8 decimal places
522 450 / 166 301 correct to 8 decimal places
208 341 / 66 317 correct to 8 decimal places
1 038 510 / 330 568 correct to 8 decimal places
30 750 000 / 9 788 029 correct to 9 decimal places
7 293 000 / 2 321 434 correct to 10 decimal places
24 491 250 / 7 795 807 correct to 12 decimal places
I would just like to point out that the polygon method has two flaws: Firstly; with each calculation in the sequence there is a rounding error. Secondly, true Pi would always be slightly bigger than a polygon with countless zillions of sides.