Simpsons and Math

I thought I'd share with you guys some subtle (and not so subtle) mathematics hidden throughout The Simpsons.

Ep: Homer the Heretic (04x04)

The characters in The Simpsons only have four fingers per hand, which would logically mean they live in a Base 8 world; however throughout the show it's clear they live in Base 10. This seems strange until it's shown that the only character with five fingers per hand is God.

Ep: The Trouble with Trillions (09x20)

Burns steals the only One Trillion Dollar Bill in existence. He gets busted by a government agent who charges him for “grand, grand, grand, grand larceny.” Since a grand is 1,000 (One Thousand), a grand grand is 1,000,000 (One Million), grand grand grand is 1,000,000,000 (One Billion), and finally a grand grand grand grand would be 1,000,000,000,000 (One Trillion).

Ep: Girls just Wanna Have Sums (17x19)

After Lisa sneaks out of the girl school and looks through the window into the boys school she sees a snowman drawn on the board. The teacher asks the students how to find the volume of the snowman. One student says to add the volume of the spheres, but Lisa points out that they forgot the volume of the nose to which Lisa exclaims, “One third base times height!”

This one isn't anything fancy, but I still liked it nonetheless. When Lisa (posing as a boy) is told to pick a fight with someone, she goes into her head and sees various math symbols. The number eight says, “Even though you’re only 8, your possibilities are infinite” as it turns to its side making an infinity symbol.

Ep: $pringfield (05x10)

Homer goes into the bathroom and finds a pair of glasses in the toilet. After picking them up and putting them on he says, “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.” This statement is an incorrect version Pythagorean Theorem.

Ep: Homerland (25x01)

After taking his ‘vitamins’ (one of which includes Crystal Math), Bart says, “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.” This is a reference back to $pringfield, and again is an incorrect Pythagorean Theorem.

Ep: Bart the Genius (01x02)

Yeah, even back in the first season they were putting equations and such into the show. Though this one isn't exactly math as much as science it is too well known not to pass up. Maggie's blocks spell out "E M C SQU" or e = mc^2.

Here has to be one of the worst math jokes I've ever heard, but here it is anyway. The teacher tells the class, “y = (r^3)/3. If you determine rate of change in this curve correctly I think that you’ll be presently surprised.” The rate of change is equal to r^2(dr) or r dr r. Which sounds like “Hardee, har har.” (It’s really bad I know.)

Ep: Fight Before Christmas (22x08)

Near the end of the episode an announcer comes on and says, “Tonight's Simpsons episode was brought to you by the symbol umlaut, and the number e; not the letter e, but the number whose exponential function is the derivative of itself.” The derivative of e^x is of course e^x. **Bonus Note: This is the episode that features Katy Perry in an extremely tight latex dress at the end.

Ep: Lisa's Sax (09x03)

When Lisa gets sent to the gifted school there are two girls playing patty-cake singing “Cross my hear and hope to die/ Here’s the digits that make pi / 3.141592653589793238462……”

Ep: Simple Simpson (15x19)

After Homer becomes Pie Man for the first time, an innocent bystander says, “We all know pi r squared, but today pie are justice, and I welcome it.”

Ep: Marge in Chains (09x21)

Apu defends his memory by stating, “In fact I can recite pi to 40,000 places. The last digit is one!" This is a true statement.

Ep: Treehouse of Horror VI (07x06)

The 3D animators had a lot of fun in this episode hiding quite a few things in the background. The first of which is a variation of Euler's Formula, e^(i*pi) + 1 = 0, which is considered one of the most beautiful formula’s in all of mathematics. There's also P = NP in the background, but unfortunately I do not know much about that.

The next thing that comes up in the background is a string of hexadecimal numbers “46 72 69 6E 6B 20 72 75 6C 65 73 21” which when translated into ASCII codes becomes “Frink Rules!”

The third involves Fermat's Last Theorem. Since this Theorem isn't as well known to people that don't enjoy math I'll explain a little bit below. Fermat’s Last Theorem was originally conjectured back in 1637 and was not proven until 1995. It states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer n > 2. In the background the equation you can see 1782^12 + 1841^12 = 1922^12, which on a standard 10 digit calculator it appears to be true. However using 3 properties of numbers we can prove this wrong pretty easily. 1. An even number raised to a positive integer power is even. 2. An odd number raised to a positive integer power is odd. 3. The sum of an even and an odd is odd. These three facts disprove the equality in the background because E + O =|= E.

Ep: Wizard of Evergreen Terrace (10x02)

Here we have another run-in with Fermat’s Last Theorem, and again it is another near miss. Oh and there’s also turning a torus into a sphere, but I don’t know anything about topology.

I hope you enjoyed!

If this is well liked and I have enough time, I would really like to go into some of the math in Futurama. Some of the sources I used:

I couldn't mention Katy Perry without showing the .gif Thanks to reddit u/RocksAndGeology for this image.