Notes for the Teacher about the pi Slides

Students are often amazed to learn that Hideaki Tomoyori, the world record holder during the making of and original airdate of this episode, knew exactly 40,000 digits. We share quotations that highlight Tomoyori's motivation and methodology, as well as a psychological study that investigated his cognitive abilities: Takahashi, M., Shimizu, H., Saito, S., and Tomoyori, H. (2006). One percent ability and ninety-nine percent perspiration: A study of a Japanese memorist. Journal of Experimental Psychology: Learning, Memory, and Cognition, 32(5), 1195--1200. Researchers compared Tomoyori to a control group and concluded that he was not superior. They attributed his achievement to extensive practice.

We also explore the motivation to calculate trillions of digits of pi. Series algorithms are used to stress test computers, and number theory questions about the distributions of the digits are much more interesting than any specific digit.

Apu was correct in the episode---the 40,000th digit of pi is indeed one, and students want to know how they ended up in an episode of The Simpsons. The writers wanted to honor Tomoyori's accomplishment and mathematician Jon Borwein first shared the story with us of how they obtained the digit. The writers enlisted the help of mathematician and computer scientist David Bailey. We show students a copy of the fax the writers sent to Bailey, which contains an image of Bart Simpson, the fourth grade son on the show. They asked Bailey for the 40,000th digit of pi. At the time, Bailey was working at NASA, and he faxed every one of those 40,000 digits. The writers told Nestler and I that they placed a huge pile of fax pages into another episode ``22 Short Films About Springfield" in honor of all those pages Bailey sent. The pile elucidates the magnitude of that many digits of pi and students laugh when we show it to them. Students are also interested to learn that research on pi continues. Bailey, along with Peter Borwein and Simon Plouffe, published a series representation of pi in 1997, and we share this with students who have taken calculus. The BBP formula can be used to compute binary digits of pi in hexadecimal notation without the preceding digits, theoretically eliminating the need for many fax pages, at least in this setting.