According to David H. Bailey and Jonathan Borwein, the number pi stands apart. Unique among mathematical constants, it captures the fascination of both professional mathematicians and the public. Pi is also, they argue, the only mathematical topic from antiquity still being researched today.
Writing in the March issue of the American Mathematical Monthly, Bailey (Lawrence Berkeley National Laboratory) and Borwein (Centre for Computer Assisted Research Mathematics and its Applications, University of Newcastle) recap the history of pi and describe recent research on whether pi is normal, that is, whether its digits are statistically random in a specific sense.
Titled “Pi Day is upon us again and we still do not know if Pi is normal,” the pair’s paper is available now from the MAA website.
A walk on the ﬁrst 100 billion base-4 digits of pi
Before they get into the math—before they explain the Salamin-Brent algorithm or discuss the benefits of displaying the digits of pi graphically as a random walk—Bailey and Borwein list a sampling of pi’s plentiful appearances in popular culture. There are piems (phrases or verse whose letter count, ignoring punctuation, gives the digits of pi), a New York Times puzzle prominently featuring the constant, and numerous television and movie cameos.
When, for instance, a 1993 episode of The Simpsons had Apu proclaiming the 40,000th digit of pi to be 1, it was Bailey who furnished the screenwriters with that fact.
The paper’s primary contribution to the literature, though, isn’t its catalog of pi sightings, or even the run-down of advances in pi-related research that follows. The take-home, says Bailey, is the argument that “modern computing technology has fundamentally changed the game for the analysis of pi and other well-known mathematical constants.”
In the paper’s conclusion, the authors note that while many basic questions about pi remain unanswered, “the advent of the computer might at last give humankind the power to answer some of them.”
Want to be prepared to appreciate these imminent advances? Get up to speed with “Pi Day is upon us again and we still do not know if Pi is normal.” Monthly editor Scott Chapman says it’s sure to be a hit.