- Reaction score
- 0
- Points
- 210
Yes, the time is upon us. Everyone knows pi day is March 14th, but any true nerd realizes pi is not 3.14, but rather an irrational constant which continues infinitely in decimal expansion. Starting at 9:26:53 (.589... sec) AM, the longest extended Pi Day of our lives will come into action. The date, at the AM and PM hours, will be " 3/14/15 at 9:26:53.589. Days like this only come once in a lifetime!
It is understood 1592 was a better year. This was probably the greatest pi day in history. Every 100 years (1915, 2015, 2115 etc) come the next closest pi days. It is also understood there are other minor pi days (be creative). Yes, 22/7 is pi approximation day -- But it's not that accurate!
In other words, 3/14/15 at 9:26:53.589AM/PM = 3.141592653589
Pi!
It is understood 1592 was a better year. This was probably the greatest pi day in history. Every 100 years (1915, 2015, 2115 etc) come the next closest pi days. It is also understood there are other minor pi days (be creative). Yes, 22/7 is pi approximation day -- But it's not that accurate!
Code:
Pi =
4*Sum[(-1)^i/ (2*i+1) ,{i,0, infinity}]
= 4*( 1 - 1/3 + 1/5 - 1/7 + 1/9-...)
This formula can be derived using the Taylor series for arctan via integration, namely arctan[x] = integral[1/(1+t^2),{t,0,x}]
and writing 1/(1+t^2) as a geometric sum with generator -t^2Pi!
