- #1
jillbones
- 2
- 0
PI(N) = N /{A * LOG(N)^2 +B * LOG(N) + C}. Note: LOG(N) is the common log.
This formula works for N up to 10^23. The accuracy depends on the number of digits
after the decimal point in the coefficients A, B & C. I used a Lotus123 spreadsheet to
calculate them. My calculated values are;
A = -0.000223480708389211732
B = 2.31221822291801513
C = -1.12554500288863357
The correct value of PI(10^23) = 1,925,320,391,606,803,968,923. The calculated value is
1,925,400,258,044,147,870,000
Not exact, but within .005%
I think that better approximations could be attained if the accuracy of the coefficients was
increased. But I have no way of testing this hypothesis
Bill J
This formula works for N up to 10^23. The accuracy depends on the number of digits
after the decimal point in the coefficients A, B & C. I used a Lotus123 spreadsheet to
calculate them. My calculated values are;
A = -0.000223480708389211732
B = 2.31221822291801513
C = -1.12554500288863357
The correct value of PI(10^23) = 1,925,320,391,606,803,968,923. The calculated value is
1,925,400,258,044,147,870,000
Not exact, but within .005%
I think that better approximations could be attained if the accuracy of the coefficients was
increased. But I have no way of testing this hypothesis
Bill J