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?
Happy Halloween! With the THOH episode behind us and the Halloween event underway, this week we take a look at a concept that has made a couple appearances in the legendary THOH episodes.
In Treehouse of Horror VI (Season 07, Episode 06), the third segment entitled Homer³ is ripe with mathematical concepts.
When Homer finds himself trapped in a three dimensional world, Prof Frink comes to the rescue:
Lisa: “Well, where’s my dad?”
Frink: “Well, it should be obvious to even the most dimwitted individual who holds an advanced degree in hyperbolic topology, n’gee, that Homer Simpson has stumbled into…[the lights go off] the third dimension.”
Lisa: [flips the light switch back] “Sorry.”
In Treehouse of Horror IX (Season 10, Episode 04), the third segment entitled Starship Poopers pays homage to Prof Frink’s quote from 3 seasons earlier.
When it’s revealed that Maggie’s real father is Kang, it leads to a custody dispute and an appearance on The Jerry Springer Show. And in typical Jerry Springer fashion, Homer and Kang get into a physical altercation that includes the following exchange:
Homer: [yelling] “You two-timing <Bleep> <Bleep!> I’m gonna <Bleep!>”
Kang: [yelling] “Oh, yeah?! Well <Bleep> hyperbolic paraboloid <Bleep> earth, your mama!”
A hyperbolic paraboloid is a doubly ruled surface shaped like a saddle or a Pringles chip. It contains two families of mutually skew lines.
In a suitable coordinate system, a hyperbolic paraboloid can be represented by the equation:
In this position, the hyperbolic paraboloid opens downward along the x-axis and upward along the y-axis. So in the plane x = 0, the parabola opens upward and in the plane y = 0, the parabola opens downward.
Due to it’s easy manufacturing and it’s inherent strength upon stacking, it is a common shape used in architecture and even snacks, as seen in Calgary’s Saddledome and the Pringles chips below:
Calgary, Alberta’s Scotiabank Saddledome
If you love math or enjoy reading these posts, don’t forget to stop by the Addicts Shop and check out all the paraphernalia, including the Math Mayhem shirts and hoodies.
Were you familiar with hyperbolic paraboloids? Did you notice the references to them yourself? Do you remember these two episodes from the show? Do you know of other real world examples of hyperbolic paraboloids? Sound off in the comments below. You know we love hearing from you.