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