# Pi Day 2016

For several years now, on March 14th, members of the SFU IRMACS Centre have observed Pi Day. Pi Day is a world wide annual celebration commemorating the mathematical constant π (pi). This year Pi Day will be on Monday, March 14th.

One of the reasons why the IRMACS Centre celebrates Pi Day is that Dr. Peter Borwein, the Founding Director of the IRMACS Centre, has had a long standing interest in the number Pi. Here are a few details that illustrate how Dr. Borwein's work is linked with the most famous of all numbers. Dr. Borwein, his brother Jonathan, and Dr. David Bailey of NASA co-wrote the 1989 paper demonstrating how to compute one billion digits of pi. This paper was awarded the 1993 Chauvenet and Hasse prizes for expository writing. In 1995, the Borweins and Dr. Yasumasa Kanada of the University of Tokyo, took pi to over four billion digits. That same year, working with Dr. Bailey and Dr. Simon Plouffe, now at the University of Quebec, Dr. Borwein developed an algorithm known as the BBP (Bailey-Borwein-Plouffe) formula to calculate the individual hexadecimal digits of pi. In other words, they were able to arrive at the *n*th digit of pi without calculating all the preceding digits. (By the way, the quadrillionth binary digit of pi is 0.) In 1999, Dr. Borwein co-authored the book "Pi: A Source Book".

The current record as of December 28, 2013 is 12 trillion decimal digits calculated by Alexander J. Yee and Shigeru Kondo. Yee and Kondo mention Dr. Borwein's work in the following way: "To verify correctness of the hexadecimal digits [in our calculations], the BBP formula was used to directly compute hexadecimal digits at various places (including the 4,152,410,118,610th place)."

Why compute the digits of Pi? In Dr. Borwein's words: "Sometimes it is necessary to do so, though hardly ever more than six or so digits are ever really needed. Whatever the personal motivations, π has been much computed and a surprising amount has been learnt along the way. The computation of Pi seems to stretch the machine and there is a history of uncovering subtle and sometimes not so subtle bugs at this stage."

**This year's Pi Day celebration will take place in the IRMACS Presentation Studio, ASB 10900, on Pi Day, Monday March 14th starting at 11:30 am. Dr. Scott T. Chapman, Professor and Scholar in Residence, Department of Mathematics and Statistics, Sam Houston State University. Dr. Chapman is the current editor of The American Mathematical Monthly. Recently, Dr. Chapman and Jonathan Borwein co-authored a paper titled "I Prefer Pi: A Brief History and Anthology of Articles in the American Mathematical Monthly".**

*Dr Scott Chapman*

### Abstract

For over 115 years, the American Mathematical Monthly has served as Mathematics’ most widely read journal for general audience papers. The Monthly holds a unique niche amongst journals in the Sciences, as its articles are intended to inform, stimulate, challenge, enlighten, and even entertain; Monthly articles are meant to be read, enjoyed, and discussed, rather than just archived. In honor of "Rounding-Up" Pi Day 2016, we review the illustrious history of this constant in the pages of the American Mathematical Monthly. Our talk will summarize two recent Monthly articles dealing with Pi: "On Pi Day 2014, Pi’s normality is still in question," by Jonathan Borwein and David Bailey; "I Prefer Pi: A Brief History and Anthology of Articles in the American Mathematical Monthly," by Jonathan Borwein and Scott Chapman.

### About the Speaker

Scott Chapman followed his undergraduate work at Wake Forest University with a master’s degree in mathematics from the University of North Carolina at Chapel Hill and a Ph.D. in mathematics from the University of North Texas. In 1987, he was named UNT's Outstanding Teaching Assistant/Teaching Fellow. During the fall of that same year, he became an assistant professor of mathematics at Trinity University in San Antonio, Texas and in 1993, he was tenured and promoted to the rank of associate professor. During his years at Trinity, he received three prestigious international fellowships from the Fulbright Commission (to Austria), the Consiglio Nazionale delle Richerche (the Italian National Science Foundation), and the Deutscher Akademischer Austausch Dienst (German Academic Exchange Service). He was promoted to the rank of full professor at Trinity in 1999. In the spring of 2003, he was only the second recipient of Trinity University's faculty-wide award for Distinguished Scholarship or Research. He has authored or co-authored over 100 publications in refereed mathematical journals or refereed mathematical conference proceedings. These papers have been co-authored with over 60 different mathematicians from nine different countries. In addition, he has co-edited two books (with a third currently in press). Many of his publications appear in some of the leading journals in algebra and number theory, such as Journal of Algebra, Journal of Pure and Applied Algebra, Proceedings of the American Mathematical Society, Bulletin of the London Mathematical Society, Discrete Mathematics, Journal of Number Theory, Pacific Journal of Mathematics, Forum Mathematicum and Advances in Applied Mathematics. His record of colloquia and invited speaking includes hour-long lectures in six different countries.

While at Trinity, he served for nine years as principal investigator and program director of the Trinity Mathematics Department's NSF funded Undergraduate Research Experiences in Mathematics Program (REU). His work with this program from 1997 to 2008 resulted in over $800,000 in National Science Foundation funding. Twenty-five of his joint publications have been written with 36 different undergraduate co-authors. Students he has directed in Trinity's REU have received or are currently pursuing graduate degrees at Harvard, Berkeley, UCLA, Rice, Chicago, Michigan, Rutgers, California Santa Barbara, Nebraska, and MIT. Three of his former research students have won NSF Graduate Fellowships. Five have attended the Tripos III Program at Cambridge. Another (Nathan Kaplan) was the 2008 winner of the AMS-MAA-SIAM Morgan Prize for outstanding undergraduate research in the United States. His record at Trinity University included a nine-year stint as Trinity's faculty representative to the National Collegiate Athletic Association. In August of 2008, he accepted a position as full professor and Scholar in Residence at Sam Houston State University in Huntsville, Texas. In September 2013, the National Science Foundation announced an award of $388,000 to Chapman to direct a new Mathematics REU Program at Sam Houston State University during the summers of 2014, 2015, and 2016. In fall of 2015 he was honored with Sam Houston State's Excellence in Scholarship or Creative Activity Award.

After a national search in 2010, the Mathematical Association of America (MAA) selected Chapman to be the 30th editor of The American Mathematical Monthly. Past editors of this publication include several noted mathematicians of the past 100 years, such as L.E. Dickson (University of Chicago), Robert Carmichael (University of Illinois), Paul Halmos (Santa Clara University), Herbert Wilf (University of Pennsylvania), and John Ewing (Indiana University). The Monthly was founded in 1896 and has been published since 1915 by the MAA. Today, the Monthly stands as the most widely read mathematics journal in the world. Of the approximately 1,000 annual submissions handled by the journal, less than 8% are accepted for publication. Chapman has appointed a diverse editorial board of 38 members. The home institutions of these members range in size from small (Bates College, Amherst College, and Williams College), to mid-sized (College of Charleston and George Washington University), to large (Penn State, Texas A&M, and Ohio State), to highly ranked (Dartmouth, Cornell, and Johns Hopkins). His editorship, which officially began on January 1, 2012, has already seen milestones. In a first for an MAA journal, Chapman has ushered in the use of a web-based submission system (Editorial Manager) for the management of submissions. In March 2013, the Monthly published the first special issue in more than 20 years featuring authors who spoke at the International Mathematical Summer School for Students hosted at Jacobs University in Bremen, Germany. His term as editor will run from 2012 through 2016. His wife, Lenora, is the Associate Vice President for Fiscal Affairs for the University of Texas at San Antonio. They spend their spare time with their sons Jonathan (17) and Cameron (15).

And, of course as is tradition, coffee and pie a la mode will be served afterwards for those that attend the talk.

Everyone is welcome!

Photos of Pi Day 2013 and Pi Day 2014

Contact: Veselin Jungic vjungic@irmacs.sfu.ca

The image above is from the animated movie Math Girl 3 “Rationalize This” by Lou Crocket and Veselin Jungic.