How I Need a Drink, Alcoholic Of Course, After the Heavy Lectures Involving ... (Videotaped lecture)

By Doron Zeilberger

Delivered March 14, 2013.

Part1   Part2
[This lecture was delivered on 3/14 (aka Pi Day), 2013 at the Rutgers University Experimental Mathematics Seminar]

Acknowledgement: The video was filmed by Brian Nakamura and edited and uploaded by Edinah Gnang

Maple package

This talk is accompanied by that studies various aspects of Pi.

Sample Input and Output Files

• If you want to see the first 1000 digits of Pi in all bases from 2 to 100, and the list of "first occurrences of 0"
the input file yields the output file

• If you want to see the first 1000 terms of the sequence of rational numbers that approximate Pi coming from the fact that the
int(x^(4*n)*(1-x)^(4*n),x=0..1);
is very small and can be expressed as A+B*Pi for some rational numbers A and B, then
the input file yields the output file

• If you want to see the first 1000 terms of the sequence of rational numbers that approximate Pi that come from the fact that the ratio Andre(n)/(n*Andre(n-1)) is very close to Pi/2 where Andre(n) is the number of up-down (aka zigzag) permutations,
the input file yields the output file

Personal Journal of Shalosh B. Ekhad and Doron Zeilberger