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?
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!”
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!
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.