Last weekend I actually did a talk on math in the Simpsons here in Melbourne and I am going to split it up into three different videos so

today get the first one nice and shot some of you will be familiar with this

first clip but I think I’ve got a few twists and turns to add to all this which will

entertain most of you. Okay, here we go: (Homer) Something you don’t see every day. Anybody lose their classes?

Last chance. The sum of the square roots of any two sides of an isosceles triangle is equal to the

square root of the remaining side. (Guy in the cubicle). That’s a right triangle you idiot! That’s great. So what does he say? Well, that. The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side. Which sounds very similar to this guy, right? Pythagoras, a squared plus b squared equals c squared. Well, it sounds very similar so what if he

actually meant to say this what were his mistakes? Well, the guy in the background already

pointed out one of them. It is not an isosceles triangle, it’s a right triangle.

What else there’s there’s other things that don’t work.

(Giuseppe) Any two sides? That’s fine so any two sides, it’s got to be those two here in Pythagoras and then there is one more which is of course… (Giuseppe) the sum of the square roots. The sum of the square roots does not work, any two sides does not work but that got me thinking, I mean Homer knows what an isosceles triangle is? That’s ridiculous! So maybe he actually did not have Pythagoras in mind. Maybe he learned it somewhere else. And there is actually another Simpsons episode that gives us a bit of a hint. where he may have learned it. (Lisa) There is new marshmellows in the Belfast charms. (Marge) No, no that’s Bart’s cereal. It’s the only way I can get him to take his vitamins. (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 it is my lines as the scarecrow in The Wizard of Oz. The scarecrow in the Wizard of Oz. Actually, if you go to the movie and you find. the (Scarecrow) The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side. Oh joy rapture, I’ve got a brain. So he says this after he’s got the brain. well you could have bad deal but maybe

not maybe maybe he’s right just because the sound similar to what I

would doesn’t mean that has to be correct that have a very very close slow

it is correct what makes not tried but two sides that have all right now what

does it say if I don’t despair of this at all of that you get out of this but

he also says you can’t do this any two sides should also be able to start of

this perspective that is scared of that too let’s also right that one now have a

look at this one doesn’t know where that it’s ok but I mean you’ve got two tons

as scared of even on two sides of the equation to what can we do it can just

cancel cancel goes and then what’s left over its gonna be equal to 0 which means

that these equal to 0 may be considered as I was trying but usually not so I

mean there’s definitely something that’s not quite right but let us forget about

this any to side business maybe maybe maybe just this once met a lot of a

beating him enter the window as reporters two things together to go but

we don’t know where to get one square roots so now we’ll have a really close

look at it and actually can do this in pictures so what does says we’ve got

like a a and B is four times as long as a and three obvious make any triangle of

anything like this so forget about it it’s big it’s not gonna

work out so it’s pretty wrong very wrong but it can get even have a look at any

China what ever you can actually get so again to get ready to square root square

holding a square here so now when we get to you we get the first time i squared

plus two times that plus so what’s the Sun squared and then we get plus can see

ok now just rearranged as a little bit and you get a + be + something but he

says is that she is a little bit longer than a and be put together so there’s a

tizzy and see a little bit longer and again it’s pretty obvious so it’s pretty

wrong also I mean this this this is a socialist triangle in the plane what

happens if you actually kind of look at triangles maybe on a on a sphere

anything like this can you actually get like 100 to work anywhere well well in the plane but really kills

this one here is the fact that in any triangle and be always add up to

something that’s bigger ditsy and basic the Scarecrow contradicts so what we’re

really aiming for is a world in which disc I here’s the triangle inequality in

and actually turns out that very hard to find anything reasonable where this

doesn’t hold the phone sample if you look at triangle honest here they also

decided so even on a three-year scarecrows work work but you know there’s a lot of

mathematicians out there who really really strange work so maybe one of you

has an idea for strange world where we can actually make us work ok but now

actually also started digging to see what I can actually find pythagoras now

pythagoras actually does pop up in this instance I know of two instances and

actually one of your mission is going to be too she got out where exactly in

those clips pops up maybe some of you actually know of other instances

scarecrow in the sense that I’d really like to know about it even other at the

movies episode of a TV episodes really

interesting running out and put in simpson’s lovers among you as a pinpoint

all the episodes of these things are ok look at first slip and see what he can

do you just like the one you know it’s false advertising no refunds paid for a

colossal good may have to do this on train before

impact but don’t get a credit crunch that 44 today

Pythagoras himself shows up as a wax android in an episode of Red Dwarf called "Meltdown" (Episode 24). Tom Baker as the Fourth Doctor quotes the Pythagorean Theorem in his first full episode titled "Robot". He does this as part of his "proof" that his mental faculties are still intact as he had just gone through regeneration…

in a alternate universe somewhere bart homer and the scarecrow are right

i dont know why Im here I can barely do math

Paint your self yellow lol

The theorem is being taken out of context; to understand it, one must consider the sarcasm of the Wizard's preceding words, which had the diploma granted the Scarecrow profound knowledge, been contradicted:

“Why, anybody can have a brain. That's a very mediocre commodity. Every pusillanimous creature that crawls on the Earth or slinks through slimy seas has a brain. Back where I come from, we have universities, seats of great learning, where men go to become great thinkers. And when they come out, they think deep thoughts and with no more brains than you have. But they have one thing you haven't got: a diploma.”

Would a spherical/rounded disk space work – with the long edge on the equator and the shorter edges crossing over the flat plane?

I wonder, could this hold true if we allowed for negative or complex side lengths?

A 45-45-90 triangle is an isosceles right triangle. In that sense, Homer is right.

I just wish he'd stop saying "square of" while pointing to the square ROOT written on the board.

This is exhibiting the humor only German mathematicians could appreciate.

Isn't that what the Scarecrow says after receiving a diploma in The Wizard of Oz? Oh there it is… LOL

Are you german? Klingt nach nem deutschen Akzent ^^

Awesome videos by the way!

The first is "David²+S.²= Cohen²" (8:13) and the second is in the giant math book at 8:28.

work hard for burkard

0:48 Perfectly cut d'ohs

The only triangle I could think of that’s true is the 45 45 90 triangle, where it’s one of the two special right-triangles. Obviously having a right angle along with two 45° angles; moreover having and a with two of the same sides having the length of 1 unit, and the hypotenuse being √2 units.

is that babushka by kate bush as your intro?

why is he acting smart and all hes doing middle school math

You neglected to consider the negative square roots at all.

The triangle inequality does have to hold in every geometry in which two points define a line segment which is the shortest curve which those two endpoints. But in those geometries the concept of 'triangle' and 'length' are really weird; if for a pair of points AB there is a point C such that AC+CB<AB, if congruency holds then there is a point D such that AD+DC<AC, and so forth, and the shortest path from A to B passes through all points; once you get there, the scarecrow theorem might not describe a fact about all isosceles triangles, but be describing a specific isosceles triangle.

There, I watched the video, now disappear from my recommendations

coughcoughbrainscoughcoughhomer and bartcoughcoughretardsThat guy's accent is so thick

If you remember what the scarecrow was lacking was self confidence. Ironic but that was directly to the point here. He sort of gained confidence in getting a brain but it really was false confidence, the wizard patronized him. Even so it made him smarter in other ways… Homer put on the glasses, he feels smart he gains one thing and loses another. You take a title it gives you a appearance of authority or to be right it is a satirical joke about the power of perception both negative and positive.

We laugh at extremely serious things we should not.

We likewise may take people who are authority's as right when they are wrong.

It is satire because we know homer from all his angles.

The moral is the dismissive nature of the mind that is inherent to human beings based on perceptions of authority in all things even knowledge.

.

Guess that is sort of the nature of reality itself, much of it depends on the orientation of were you are, when you see things is how you perceive things. So that you could be wrong even if it appears right objectively but it is really a matter of relativity. A oval cone from afar might appear to be a triangle. In such a case i suppose the argument becomes is it a triangle or isn't it, but now were talking about the resolution of the context of information, relativity seems to apply everywhere even for this joke so that there is a limiting factor in being right that depends on from what point or points of view you are speaking of as valid.

Inside of a sphere? Where c is closer to the 'equator'

What c squared equals a squared plus b squared minus 2 times a times b times cosine of opposite angle of c?

The solution is sqrt(1/e) + sqrt(1/e) = 2 × sqrt(1/e) or (1 – sqrt(1/e))

The number approx 0.367…

The Pythagorean Theorem but it's the opposite day

"european improves animation with numbers"

An isosceles triangle can be a right triangle, though.

81sqroot+256sqroot=625sqroot

Inverted sphere?

Alright recommended videos. You win this one.

NEEEEEEEEEEERD!

5:49 But c

isa little bit longer than a and b put together. How long is 2Sqr(a)Sqr(b)?It works with a strand of DNA Euclidean geometry – where's my award? 🙂 Send it to me on a "5 sided square" <—- take that in folks – just take it in <3

16a^2=2a^2+2a^2cos(theta)

2cos(theta)=14

cos(theta)=7

That's why such a triangle doesn't exist

Can we turn the background black? Or blue? Kills my eyes at night

obvious answer: it's the pythagorean theorem.

If you subtract the second equation from the first, …

√a+√a = √b

√a+√b = √a

√a+√a-(√a+√b) = √b-√a

… you get

√a-√b = √b-√a,

which means that a = b.

Erdös used to go up to other mathematicians at the end of their 15-minute presentations at graph theoretical conferences, wave his notebook, and say, "I've just proved that almost all graphs are counterexamples to your conjecture." This is even worse: ALL triangles are counterexamples to this "theorem."

Dear Mathologer: Although this is not relevent to your fascinating lecture,can you suggest a way to solve the following?.The nearest I got was in trying to produce a quartic equation………………..the square root of x +y =7. the square root of y +x =11. find the numerical value of x and y.

Homer was quoting the scar crow after he got his deploma at the end of the Wizard of Oz.

Square root of any side of an equilateral triangle is equal to the square root of any of the two remaining sides. 🙂

But A+B < C does work on a sphere. You just have to go the long way around the sphere. So the Mercator projection would look like ____________/______________Edit: I'm sure you've gotten this a thousand times. I tried to find a similar comment, but if it's not in Top Comments… I'm not sifting through that S— pile, lol

A right triangle CAN still also be isociluse

It works if it's an equilateral triangle with a side length of 1

1. E = mc^2

2. c^2 = E/m

3. a^2 + b^2 = c^2

4. a^2+b^2 = E/m

5. Profit!

Cool Video!

I know it was refraction at first, its the second part of the question thats hard to answer.

A 2x longer, not 4x

Danil Dmitriev, спасибо

Because the people that do cartoons studied graphic desing not math.

@6:14 take a cone, that's height is more than ~2,9782 times longer than it's circle base's radius, so the triangle is drawn on the surface of this cone, like one peak of the triangle is the tip of our cone, then we take two opposing points on the base arc and make them the other two points. Three points, three edges 😛 Okay it's basicly a robe as we unfold it to 2D. But, at least i tried! 🙂

Did anyone mention Simpson's rule on the show?

It's important to pay attention in calculus class. Someday you might be working in a metal shop and the boss will tell you to cut a wire in two, and bend one piece into a circle and the other into an equilateral triangle, and make sure the total area of both shapes is as big as possible.

if you take an hyperbolic plan build on a cone with an angle enough close to 2π, I think you can make a triangle that will satisfy the condition of a+b<c. Because you cant obtaint a and b almost or totaly right (in sens of Euclid plnas) and c curved.

It can be made to work on the sphere, but you are kind of cheating. Normalizing for the unit sphere, a = b = 1/2 pi, c = 2 pi

The problem as originally shown in the cartoon panel makes no reference to any geometric construction, and as depicted is universally correct. If we let square root of a = 3, and square root of b = 7, then square root of c = 10. Now, substitute any value you wish for square root of a and square root of b. Square root of c will then simply be the sum of those 2 values. ( Test my argument with any real numbers for square root of a, and square root of b – numbers do not have to be integers, can be both positive, both negative, or one of each )

IF, on the other hand, the cartoon representation is not what you meant – we could backtrack and start with the statement that the square root of the sum of 2 squares is NOT the sum of the square roots of the 2 squares.

Proof of my statements above is left to the student. (N.B. – Pythagoras' theorem is "The square root of the hypotenuse of a right triangle equals the square root of the sum of the squares of the 2 adjacent sides")

How to easily prove that this is a contradiction: √a+√b=√c, so if we square both sides we get: a+b+2√(ab)=c. But, from triangle inequality a+b>c, so if we substitute we get c+2√(ab)=c, and if we cancel out the C's, we get 2√(ab)<0, which is a contradiction.

Edit: I didn't watch the proof in the video yet.

His laugh is adorable. Love it!))

The theorem could work if the triangle was placed in a spherical cube where it’s centroid is at the vertex of the spherical cube plane.

What about an isosceles right triangle? It would satisfy the "right triangle" requirement and the "isosceles triangle" requirement. Unfortunately it doesn't satisfy the "any two sides" requirement.

A sector with central angle 229.183 degrees and radius 1 gets arc length 4. Square root 1 plus Square root 1 equals Square root 4.

Maybe in a pseudo sphere

√a + √b = √c for a right triangle isn’t incorrect if a b and c are define to al be of the fourth root.

Your diagram looks like bart's head.

"The sons of the squaw on the hippopotamus hide is equal to the sum of the sons of the squaws on the other two hides."

There are 2 complex solutions to that equation if you try to find the cosine of the equal angles which is 2.

@7:10 you show us that on a sphere triangle inequalities a + b > c is true but if you take c on the other part of the circonpherence (also draw in grey) you have a tirangle that a + b >c is false.

in fact you take two plane one pass by equator and the other pass by poles (2 plane perpendicular each other) you have a triangle (biangle seem too be more exact cause on off the angle is 180°) that a+b=c

may a make a mistake, i'mnot a mathematician but just with my instict i'm pretty sure that i'm not wrong (and i already draw and mesure it on a tennis ball)

to be fair: the scarecrow got a perfectly working brain. Probably could run for us president with it

[Nerd Alert] My God. This is a prime example of why people make fun of nerds. They are obsessed with the "Must solve the equation" or "the equation must solve". It does not even occur to them that an equation posted on the screen or paper, may in fact be deliberately wrong to prove the point of a conversation and/or in this case, help add to the comedic value of the moment.

Math nerds need go find a dictionary, and look up some new terms to memorize . . .

Sarcasm,

Irony,

Faux pas,

Some things in life are used improperly to add to the moment. 1 million + views yet only 1269 comments. People came because of human curiosity or the need for some Ha Ha in their life.

Congrats, you managed to suck both of those completely out of the moment.

If there's 3 things I can stand . . . it's people that can't count !

Reminds me of the Optimist's Theorem: √(a^2 +b^2) =(a +b).

Simpson’s have many times shown controversial predictions and statements

If Simpson say I guess there is at least one such triangle

It would be fun if it worked on a donut surface… 😉

I don't think topology would allow that for any spce, as weird as it might be.

Español: el teorema de homer

Demas hispanohablantes: https://bit.ly/2YAdm8u (Es una imagen, abrelo xd)

A rt angled triangle with the sides opposite and adjacent being equal in length – is also an Isosceles triangle.

aww i was hoping you'd immediately cover the case of hyperbolic topology =} i dont understand it that well

I think Futurama has more Math in it then the Simpsons one of its creators holds a PhD in Math & Physics.

It's never true. b=2×a×cos(theta/2)

sqrt(b)=sqrt(2×a×cos(theta/2) cannot be equal to 2sqrt(a) because cos(theta/2) is never equal to 2. Theta being the angle between the isometric lines

PLEASE DO THE MATHS FROM REGULAR SHOW! more specifically the scene where rigby dreams of getting his diploma and the other episode where he drinks “smarter juice” !

El título me salía en español, me siento engañado

It is maths. The word is plural, not singular.

3:01 Is he sure he's not him?? They look very similar

There is a right triangle that is an isosceles triangle, so the argument is correct.

@ 4:20 there is something green written on his hand.

If you put a triangle on a sphere and then strech one side around more than half the circumference, you can get a triangle where sqrt(a)+sqrt(b)=sqrt(c)

In a complex plane?

mhh…. I was waiting for the proof that √a + √b = √c could not be solved for any nonzero whole numbers. Or can it?

I have discovered a truly marvellous proof of homer’s theorem, however this comment box is too small to contain it.

It should work on a toroidal. I have imagined the triangle embracing the lap

4:19 A handful of notes.

On a sphere when: c > π·r

Please look at EPISODE 9 from 12 -TEMPORATED WHERE HOMER GETS INTELLIGENT! Aah!

😉✌👋

What about when dealing with side lengths all less than 1?

if you collapse b to zero, in the limit the second case works. the first case only works in a moebius strip.

One instance where it works? Lets say the circumference of the sphere is 2… Lets have the side c be equal to maybe 1.5 and then the other two sides can just connect from the end points of the side c… That would make a+b<c which would work for the scarecrow theorem

a+b=<c could work if the plane had 3 dimensions and you looked at it at an angle. ie, a projection.

If c is nearly as big as the circumference of the sphere you could make a triangle where (a+b)<c.

heheehe for all this the solution is a dorito's chip …if you cannot see it lmao