Morning Mathematical Monsters & Maniacs!
(Today’s post is sponsored by the letter “M”)
Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.
And what better way to start your week, then by discussing math Monday morning?
In a few days (3/14), the world will commemorate Pi Day. And in honour of Pi Day, this week we’re going to look at occurrences of Pi in The Simpsons. This post was also scheduled for 3:14pm UTC in honour of Pi (still morning in Toronto though).
In mathematics, Pi is a mathematical constant (definable) and irrational number (a number that does not terminate, nor does it repeat). Since the mid-18th century, Pi is also expressed by the Greek symbol π. It was Swiss mathematician Leonhard Euler (who we discussed in Math Mayhem 04) who first published π in 1736. Prior to this, it was better known as Archimedes’ constant, after the 3rd century BC Greek mathematician (Archimedes pictured below).
Even before Archimedes, π was approximated over 3,000 years ago by ancient Egyptian (≈3.1605), Babylonian (≈3.125), and Indian (≈3.139) civilizations. However, it was Archimedes who was the first to create an algorithm to calculate π. He used a geometrical approach to calculate π that was used for over 1,000 years. Archimedes computed upper and lower bounds of π by drawing a regular hexagon inside and outside a circle, and successively doubling the number of sides until he reached a 96-sided regular polygon. By calculating the perimeters of these polygons, he determined π was between 3.1408 and 3.1429. By 1630, Archimedes geometric approach using hexagons allowed π to be calculated to 39 decimals.
The calculation of π was revolutionized by the development of infinite series techniques as long as 500 years ago. The discovery of calculus, by English scientist Isaac Newton and German mathematician Gottfried Wilhelm Leibniz in the 1660s, further led to the development of many infinite series for approximating π.
With the advent of the computer in the mid-20th century, the calculations of π jumped leaps and bounds from 1,120 decimal places in 1949 to 7,480 decimal places in 1957 to 10,000 decimal places in 1958 to 100,000 decimal places in 1961; until 1 million decimal places were reached in 1973.
π was originally defined as the ratio of a circle’s circumference (C) to its diameter (d):
π = C/d.
Regardless of the size of the circle, the circumference is always 3.1415926535897932384626433… times bigger than the diameter.
Because π is closely related to the circle, it is found in many formulae from the fields of geometry and trigonometry. Other branches of science, such as statistics, physics, Fourier analysis, and number theory, also include π in some of their important formulae. Some notable formulae involving π include:
The circumference of a circle with radius r is 2πr.
The area of a circle with radius r is πr2.
The volume of a sphere with radius r is (4/3)πr3.
The surface area of a sphere with radius r is 4πr2.
π has made numerous appearances on The Simpsons over the years. Here are some notable appearances:
In Season 4, Episode 24 Marge in Chains, Marge gets busted for accidentally shoplifting at the Kwik-E-Mart. During the subsequent trial, when being questioned by Lionel Hutz, we get the following line:
Apu: “In fact I can recite pi to 40,000 places. The last digit is one!“
Homer: “Mmm, pi(e).“
For those curious, the 40,000th decimal place of π is indeed a 1. However, reciting to 40,000 decimal places isn’t that impressive. The record for memorizing digits of π, certified by Guinness World Records, is 70,000 decimal places, recited in India by Rajveer Meena in 9 hours and 27 minutes on March 21st, 2015.
In Season 9, Episode 3 Lisa’s Sax, the family recounts the story of how Lisa got her instrument during the terrible heat wave of 1990. During the episode, two girls at a gifted school play patty-cake while chanting the digits of π: “Cross my heart and hope to die / Here’s the digits that make pi / 3.1415926535897932384….”
In Season 12, Episode 16 Bye Bye Nerdie, Lisa’s attempts to befriend Francine, a new student at Springfield Elementary, result in constant bullying. This leads her on a crusade to find out just what makes bullies “tick.” Lisa takes her findings to the ’12th annual big science thing’ where she reveals the cause of why bullies beat up nerds. Prof. Frink addresses fellow scientists at the conference.
Prof. Frink: “Scientists … Scientists, please! I’m looking for some order. Some order, please, with the eyes forward and the hands neatly folded and the paying of attention. Pi is exactly three!”
Prof. Frink: “Very sorry that it had to come to that, but now that I have your attention, we have some exciting new research from young Lisa Simpson. Let’s bring her out and pay attention.”
The most memorable appearance may be in Season 15, episode 19 Simple Simpson, when Homer becomes a masked superhero known as the “The Pie Man”. He uses pies in order to battle crime in Springfield.
Homer, disguised as Pie Man, throws a pie at Rich Texan, to which Drederick Tatum states “We all know “pi r squared,” but today, “pie are justice.” I welcome it.”
In the same episode, Kent Brockman reporting states: “Pi! Popular pastry, tricky math thing, and now sword of righteousness. A masked avenger has been giving Springfield’s scoundrels their [chuckle] just desserts.”
In Season 26, Episode 22 Mathlete’s Feat, The Springfield Elementary School Math team wears shirts that highlight the irrational nature of π by stating π cannot be expressed as a fraction.
The episode also features a mathematical joke:
Now we know more about one of the most famous constant and irrational number in mathematics. Pi Day often comes with specials at bakeries and pizzerias on pies and pizzas, usually on sale for $3.14. Will you be commemorating Pi Day? Were you familiar with π? How many digits of π do you have memorized? Did you notice π in these episodes? Were you able to solve the joke in the last screenshot? Sound off in the comments below. You know we love hearing from you.