Class Opener – Day 70 – A “Homer”ic Effort

I confess – I was a bad person today. And here’s why….

One of my recent reads is Simon’s Singh‘s fun book The Simpsons and Their Mathematical Secrets, where Simon shares math gems from Simpson’s episodes hidden craftily by the math-centric series writers.

I confess I haven’t been a regular watcher of the Simpson’s for many years. This book took me back to the fun of many of the early episodes – like the corny “R D R R” gag from season 1.

One of my favorite math memories from the Simpsons is the early “Treehouse of Horror” episodes, where Homer is sucked into a strange “3D” world. It’s from this episode which I shared a screen-grab from the strange “Tron-esque” world as today’s class opener:

My math radar always goes off some when I see math included in movies or TV. Who exactly is providing the math – do they know anything about what they are sharing?  Here, we are presented with an interesting equation:

Where the heck did they get that from? Is it just gibberish? Is it even true? (note – this is exhibit A as to why I was a bad person today – of course I know where it came from, but it’s time to dangle the bait in front of the kiddies)

Many students dove into their calculators to verify the equation, and there were quite different results:

In my morning class, a few students quickly “verified” that the equation was true, and the rest trusted them. Bless them…..I can now dangle more bait….

In my afternoon class, students were a bit more careful. You’ll find that the two sides of the equation share many leading digits, but the equal-ness falls apart in the later digits. One cunning student dicovered the Nspire will give a conclusive “false” when presented with the equation. This is shown below, along with the full calculations:

So now, exhibit B of “I am a bad person”. I then gave both classes the following challenge: I will give you a candy prize if you can name any positive integers which satsify the following:

, where n is a positive integer greater than 2.

I really admire the students who tried here, even those who pretty much ignored anything else we were trying to get done. The agony when they came oh so close to a solution, only to see it break apart. I really can’t let this go on, can I?

STUDENT: Do you have any advice for us? Please?

ME: Yes…give up.

STUDENT: Come on…give me a hint here.

ME: I am…give up, it’s the best advice I can give you.

Letting students off the hook, we shared a brief discussion of Fermat’s Last Theorem, and why the Simpsons’ folks were so clever with this “near miss” in their Halloween episode.  Many stayed behind after class to hear more about some of math’s long-standing mysteries, and how exactly Fermat’s Theorem was eventually proven. After my bout of evilness, it was a pretty cool day.