Returning more than 12 digits for a result

[Gerson W. Barbosa]

(03-18-2018 08:15 AM)brickviking Wrote:  I ran across this video about manually calculating pi yesterday, and I decided to run that formula through my calculator (the Chudnovsky algorithm). I

Here's the formula for those of you brave enough to enter it in:

'426880×SQ(10005)/⅀(K=0,2,(6×K)!×(545140134×K+13591409)/((3×K)!×K!^3×(-262537412640768000)^K))'

The funny "⅀" symbol is SUM (RS-SIN) and the "×" is * (multiply) for those of you that don't have fully-working Unicode fonts.

Interestingly the double of 13591409, one of the integer constants in the formula, equals to 27182818, as noticed by someone in a comment to the video. This leads to (5000000 - pi/60)*e = 13591408.99996632, a remarkable coincidence.

No bravery is required for just copying and pasting the formula. Anyway, here are the results for various k, for checking purposes:

0: pi - 5.90E-014
1: pi + 3.08E-028
2: pi - 1.72E-042
3: pi + 1.00E-056
4: pi - 5.96E-071
5: pi + 3.61E-085
6: pi - 2.21E-099
7: pi + 1.37E-113
8: pi - 8.51E-128
9: pi + 5.33E-142


426880×SQRT(10005)/SUM(K=0,2,(6×K)!×(545140134×K+13591409)/((3×K)!×K!^3×(-262537412640768000)^K))

SQ has been replaced with SQRT to avoid confusion with x^2.