Super Safi’s Monday Morning Math Mayhem 25 – Hyperbolic Paraboloid

Morning Mathematical Monsters & Maniacs!

(Today’s post is sponsored by the letter “M”)


Hi, I’m Super Safi and you may remember me from such stats and strategy posts as Kwik-E-Mart Farming and the advanced losing-to-win Superheroes battle strategy.

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!


Hyperbolic Paraboloids

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

Pringles Chips



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.

10 responses to “Super Safi’s Monday Morning Math Mayhem 25 – Hyperbolic Paraboloid

  1. I’ve talked about these in my Calculus III class! They’re good examples that illustrate the concept of saddle points.

  2. Future post idea: 24 hour task for God (reward: $777,777), then converted to Rat Trap Truck XP with the Collider running – at what bonus % does it generate more donuts than it costs to rush the task (260, I believe?) A perpetual donut machine, if you will (in this house we obey the laws of THERMODYNAMICS!!)

  3. Hyperbolic paraboloid, ay?
    Sounds like a disease.

    • My multiplier is 3713. The math produces a ridiculous number of donuts (38k) from buying rat trap trucks. I have $2.6B and when I tap tomorrow, I should double my money. Can there be too much of a good thing.

  4. Question, I finished the first quest late Friday, but the second set of quests have not launched. Are they staggered release dates? Or am I just having an issue?

    • Like all events with multiple Acts in TSTO, each Act is triggered by different start times. As laid out in multiple posts (and in the Event Page), each Act is staggered to start weekly (typically on a Wednesday).
      In the case of the Halloween event, Week 2 starts automatically on October 30th.

  5. Thanks Safi for sneaking in a Calculus reference used in a Simpson’s THOH Episode (spoken by an 👽)😉👍

    It’s a shape used in architecture – especially my favourite – mid century modern and you can find examples all over Las Vegas / Southern California.

    Let’s see if we will get some more THOH in this Event before further chaos results 😅

  6. I’m very happy because i bought the ‘wailing wall’ for only 1000 $ but kow i see it in the store fo 50 donuts ahahahah

    • *now – for

    • Go ahead… rub it in…. put salt in the wound.. ‘stack’ it up Bud-dy… I guess it was only hours that the glitch existed… lol.. and I missed out on it…

      — Safi, those 2 episodes are hilarious.. i do recall more Math equations flying by when Homer is in the 3rd D. . The Simpsons, is there anything they can’t do?!…

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