“Cross my heart and hope to die. Here’s the digits that make pi: 3.1415926535897932384…” Simpsons —From “Lisa’s Sax”

Sarah J. Greenwald Rule! Appalachian State University Andrew Nestler Santa Monica College

ow in its 14th season, The Simp- Pythagorean Theorem. sons is an award-winning global [Actually, borrowing again Season One DVD Collection. Season One DVD Npop culture phenomenon and the from a great movie, he longest-running sitcom in television his- recites, verbatim, what the tory. Did you know that The Simpsons Scarecrow says in the film also contains scores of instances of The Wizard of Oz upon

All photos courtesy Fox Home Entertainment & The Simpsons mathematics, many designed to expose receiving his “brain.”] and poke fun at innumeracy? Several Homer: The sum of the square roots Police Chief Wiggum: Whoa, episodes of The Simpsons contain signif- of any two sides of an isosceles whoa—slow down, egghead! icant mathe- triangle is equal to the square root Frink: ...but suppose we extend the Al Jean, Executive matics, with of the remaining side. square beyond the two dimensions Producer and head material Man in stall: That’s a right triangle, of our universe, along the hypo- writer of The ranging you idiot! thetical z-axis, there. Simpsons, has a from arith- Homer: D’oh! Everyone: [gasps] bachelor's degree in metic to 3 Frink: This forms a three-dimen- mathematics from In the segment “Homer ” of the 6th geometry to sional object known as a “cube,” Harvard University. annual Halloween episode “Treehouse calculus. or a “Frinkahedron” in honor of its Of Horror VI,” Homer disappears into a There’s discoverer, n'hey, n'hey. wall in the living room, and his family even a resident mathematician and inven- Homer's voice: Help me! Are you and friends gather to try to rescue him. tor, Professor Frink. helping me, or are you going on Here we present some of our favorite Lisa: Well, where's my dad? and on? mathematics from the series. You can Professor Frink: Well, it should be Frink: Oh, right. And, of course, check out our extensive guide to this obvious to even the most dimwit- within, we find the doomed indi- subject online (http://simpsons ted individual who holds an vidual. math.com). We hope that you enjoy advanced degree in hyperbolic Here the characters appear to be assum- these memorable mathematical moments topology, n'gee, that Homer Simp- ing that their world is two-dimensional; from The Simpsons, and along with us, son has stumbled into the third later in the same episode they behave as if keep your eye out for still more in the dimension…. it were three-dimensional. years to come. Frink: [drawing on a blackboard] Here is an ordinary square.... Arithmetic and Number Theory Geometry and Topology One of the equations rushing past In the episode “$pringfield (Or, How I Matt Groening, creator of The Homer in his strange 3rd dimension is Learned to Stop Worrying and Love Simpsons,grew up in Portland, 178212 + 184112 = 192212. Legalized Gambling),” a take-off on the Oregon, with a father named subtitle of Dr. Strangelove, Homer finds Homer, a mother named Marge This equation is false. Yet, some of our a pair of eyeglasses in a men’s room toi- and sisters named Maggie and students think it is true since a TI-83 gives let, and upon putting them on, recites Lisa. the 12th root of the left-hand side as 1922! what he presumably believes to be the Continues on page 16 MATH HORIZONS

Don’t you get it, Bart? Derivative dy = 3r2 dr/3, or r2 dr, or r dr r. Har de har har! Get it?

David X. Cohen, who served as a writer for The Simpsons for almost five years before creating Futurama, has a bachelor's degree in physics from Harvard University and a master's degree in computer science from UC Berkeley.

Continued from page 2 Frink: Very sorry that it had to come Probability In “Guess Who’s Coming To Criticize to that, but now that I have your In “Dog Of Death,” a TV ad for the state Dinner?” the children take a field trip to a attention, we have some exciting lottery is shown, featuring office work- major newspaper publisher. new research from young Lisa ers in a skyscraper. Simpson. Let's bring her out and Newspaper editor: … And to Employee: I don't need your crum- pay attention. protect Mother Earth, each copy my job, Mr. Employer! I've won contains a certain percentage of In the episode “Marge In Chains,” Apu the lottery! recycled paper. and Homer discuss π Employer: Well, who needs employ- Lisa: And what percent is that? ees? I won the lottery, too! Apu: In fact I can recite π to 40,000 Newspaper editor: Zero. Zero’s a [Two window washers descend on a places. The last digit is one! percent! scaffold, each with a huge bag of Homer: Mmmm, pie. cash at his feet] In “Bye Bye Nerdie,” Lisa asks Nelson If you use a computer algebra program Window washers: We both won the why another bully attacks only nerds. to check this, you will see that Apu is lottery! Lisa: Why does she only go after the correct. All [to camera]: Why don't you win smart ones? the lottery, too! Nelson: That's like asking the square Calculus Announcer: The state lottery—where root of a million—no one will ever In “Bart The Genius,” fourth-grader Bart everybody wins! (Actual odds of know. cheats on an aptitude test, and is subse- winning: 1 in 380,000,000.) quently transferred to a school for gifted Of course, we In the same episode Prof. Frink addresses children. fellow scientists at a conference. estimate your 3 Teacher: So y = r /3 and if you deter- odds of laugh- Prof. Frink: Scientists...Scientists, mine the rate of change in this ing along with a please! I'm looking for some curve correctly, I think you’ll be mathematical order. Some order, please, with the pleasantly surprised. moment on The eyes forward and the hands neatly [The class laughs.] Simpsons to be folded and the paying of attention. Teacher: Don’t you get it, Bart? much higher π 2 2 is exactly three! Derivative dy = 3r dr/3, or r dr, than that! ■ [crowd gasps] or r dr r. Har de har har! Get it?

16 APRIL 2003