Super Safi’s Monday Morning Math Mayhem 06 – Pythagorean Theorem

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?

This week, we’re going to look at one of the most iconic quotes in cinematic history, that has appeared on the large screen, as well as on the small screen in a couple of The Simpsons episodes, and on the even smaller screen quite recently in Week 1 of our Valentine’s 2019 Tapped Out game.


In The Wizard of Oz, a 1939 American musical fantasy film produced by Metro-Goldwyn-Mayer and widely considered to be one of the greatest films in cinema history, when the Scarecrow gets his diploma (instead of a brain) from the Wizard, he says the following:

The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.


In Season 5, Episode 10 $pringfield (Or, How I Learned to Stop Worrying and Love Legalized Gambling), Homer finds Henry Kissinger’s glasses in the men’s room toilet, puts them on, and puts his finger on his temple like the scarecrow in The Wizard of Oz.

Homer: “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.

Man in stall: “That’s a right triangle, you idiot!

Homer: “D’oh!


In Season 25 premiere Homerland, Marge reveals that Bart’s prescription medications include Crystal Math.

Bart: “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.

Lisa: “That’s not right.

Bart: “Yes, it is, they’re my lines as the Scarecrow in ‘The Wizard Of Oz.’


And most recently, in Week 1 of this current Valentine’s Day Event, in Lisa Live Pt. 4, we get the Scarecrow quote from Ralph:

Lisa: Skinner was using me!
Mr. Bergstrom: But you were TEACHING, Lisa! Listen to Ralph.
Ralph: The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.
Mr. Bergstrom: He was supposed to be learning history, and the math is all wrong… but still!


Pythagorean Theorem

For someone who asked for brains, the Scarecrow should ask the Wizard for a refund. He really got jipped. His formula of the Pythagorean Theorem is wrong for many reasons. One of the reasons is, as the man in the toilet stall pointed out to Homer, the Pythagorean Theorem applies to right triangles, not isosceles triangles. Secondly, the Pythagorean Theorem is about the squares of two sides in relation to the square of the third side, not square roots. And thirdly, the Pythagorean Theorem is dependent upon the two sides, and can not be applied using any two sides.

The Pythagorean Theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the “Pythagorean equation”:

a2 + b2 = c2,

where c represents the length of the hypotenuse and a and b the lengths of the triangle’s other two sides.

The theorem is named after the ancient Greek mathematician Pythagoras, pictured in the bust below, who lived around 570–495 BC. He is credited with its first proof, although no evidence of it exists. There is some evidence that Babylonian mathematicians understood the formula, although little of it indicates an application within a mathematical framework. Mesopotamian, Indian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases.

Some common numbers first taught to school children for the formula a2 + b2 = c2, include triangles with sides 3, 4, and hypotenuse 5 and sides 5, 12, and hypotenuse 13:

32 + 42 = 52,     9 + 16 = 25

52 + 122 = 132,     25 + 144 = 169

The Pythagorean Theorem has been given numerous proofs – possibly the most for any mathematical theorem. The proofs are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and indeed, to objects that are not triangles at all, but n-dimensional solids.



The Pythagorean Theorem makes a couple more appearances in The Simpsons. In the Season 7 Treehouse of Horror VI episode, co-producer David S. Cohen’s name uses the Pythagorean equation. As well, in Season 18, Episode 20 Stop or My Dog Will Shoot!, Bart is tormented in his dreams by a math book that features the Pythagorean equation on the cover.


Now we know more about one of the most famous lines to appear on the big screen, small screen, and our Tapped Out screens that messed up one of the most famous mathematical equations of all time. As well, the correct mathematical equation.

Were you familiar with the Pythagorean Theorem? Were you familiar with the erroneous Scarecrow version? Did you notice that Homer and Bart were quoting the Scarecrow on the show? Did you catch Ralph saying the formula in our games during Week 1 a couple weeks ago? Sound off in the comments below. You know we love hearing from you.

18 responses to “Super Safi’s Monday Morning Math Mayhem 06 – Pythagorean Theorem

  1. Hey, Safi. I posted this recently, but I think nobody will be going back to the article I posted it in. Therefore, I am copying it here to get your “math jedi” thoughts…I searched and couldn’t find anything, so either an article has not been written about it before, or my search skills are sub-average, hehe. But, I send the majority of KrustyLand ticket earners on 24 hr jobs there (or just 12 in the case of some players). I don’t send railyard earners there, and during events, I don’t send the characters used for event earning. So, my question is, do you generate more in-game cash for sending them to KL and then exchanging tickets earned for cash or do you earn more for sending them on 24 hr jobs in Springfield? I’ve recently started KEM farming, and I’d like to keep my cash high. I haven’t cashed in my tickets since the whole KL event, so I have a ton. I’m saving them just in case, hehe. But, as I’ve been reading many articles on KEM farming, I always see that you need to keep cash up, but it never mentions using KL tickets as a way to generate cash (in addition to all the buildings there that generate tickets every X hours). So, I know the math is relatively simple, but I was curious if people use this exchange to keep their cash up, and if they find it more valuable to send players there (it takes more time bc you can’t just use the job office to send them there – on that note, EA, why can’t there be a KL job button to send all KL characters on jobs there?!). Anyway, thanks for any thoughts, and the long post is officially over!

  2. Oh Great Safi, Master of all things mathematical, tell us the formula for always choosing the 3 donut mystery box!!!

    • The formula for choosing 3 donuts each time is simple. It can be expressed by the following formula: 3d = (a U b U c) ^ M(H^o) – pi (1/137)^8 x sqrt(hc/G) ; where 3d is 3 donuts, a is the left box, b is the middle box, c is the right box

  3. This takes me back about 45 years ago, to 10th grade Geometry class. Our teacher was Mr. Gregory and he used to box in his younger days so all the cartilage in his nose was broken and he could flatten his nose and smoosh It all around. The boys thought it was cool, the girls, not so much. Funny, the things that linger in the hidden recesses of your brain.

  4. Is anyone having Login issues?

  5. Tracy-1ltwoody920

    I recall watching WoOz as a child and my smarmy older sister declaring “I know that”, or something along those lines.
    Two years later, we again watched the movie, and when I heard the Scarecrow utter those words, I thought,
    “ what did he say.”
    “doesn’t sound right”
    “But my wise older sister agrees, so I must be wrong”

    Took me YEARS to realize how idiotic I was.

  6. This equation I remember….I had completely forgotten when to apply it properly. That’s pretty funny that the Scarecrow had it wrong and The Simpsons writers have noted it multiple times!
    I remember doing what seemed like endless numbers of proofs in Trigonometry…the teacher was one that taught us to memorize and spew the right answer, but not Why it was the right answer. It wasn’t untill I got a Better teacher the next year in Geometry that any of it made any sense what so ever.
    So to Ms. Scott, where ever you are, thanks for nothing! 🤯

  7. Thanks a lot Safi! This posts are awesome as always 😀

  8. I sometimes find myself wondering: Do the show writers also write the dialog for the TSTO game skits? Because I can think of no more obvious explanation for the same quote (and corresponding correction) to appear in the game.

    It would actually be kind’a cool if the answer is yes… but it would be an intriguing mystery connection, if the answer is no. (Not sure which I actually *want* it to be, come to think of it…)

  9. Interestingly enough and almost coinciding with Monday Morning Math Mayhem, my Argyle Sweater desk calendar, for Saturday/Sunday poked fun at Fibonacci! (Wish I could upload a pic)

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