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

Math in the Simpsons: Homer’s theorem

100 thoughts on “Math in the Simpsons: Homer’s theorem

  • April 17, 2019 at 11:39 pm
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    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…

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  • April 17, 2019 at 11:39 pm
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    in a alternate universe somewhere bart homer and the scarecrow are right

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  • April 18, 2019 at 3:24 am
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    i dont know why Im here I can barely do math

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  • April 19, 2019 at 3:15 pm
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    Paint your self yellow lol

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  • April 20, 2019 at 7:28 am
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    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.”

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  • April 20, 2019 at 2:38 pm
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    Would a spherical/rounded disk space work – with the long edge on the equator and the shorter edges crossing over the flat plane?

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  • April 20, 2019 at 2:58 pm
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    I wonder, could this hold true if we allowed for negative or complex side lengths?

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  • April 20, 2019 at 5:56 pm
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    A 45-45-90 triangle is an isosceles right triangle. In that sense, Homer is right.

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  • April 20, 2019 at 10:47 pm
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    I just wish he'd stop saying "square of" while pointing to the square ROOT written on the board.

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  • April 21, 2019 at 7:09 am
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    This is exhibiting the humor only German mathematicians could appreciate.

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  • April 21, 2019 at 4:42 pm
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    Isn't that what the Scarecrow says after receiving a diploma in The Wizard of Oz? Oh there it is… LOL

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  • April 21, 2019 at 4:52 pm
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    Are you german? Klingt nach nem deutschen Akzent ^^
    Awesome videos by the way!

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  • April 21, 2019 at 9:52 pm
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    The first is "David²+S.²= Cohen²" (8:13) and the second is in the giant math book at 8:28.

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  • April 22, 2019 at 7:55 am
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    work hard for burkard

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  • April 22, 2019 at 5:19 pm
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    0:48 Perfectly cut d'ohs

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  • April 23, 2019 at 3:05 pm
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    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.

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  • April 23, 2019 at 5:14 pm
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    is that babushka by kate bush as your intro?

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  • April 24, 2019 at 2:07 pm
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    why is he acting smart and all hes doing middle school math

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  • April 24, 2019 at 9:33 pm
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    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.

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  • April 25, 2019 at 9:16 pm
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    There, I watched the video, now disappear from my recommendations

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  • April 26, 2019 at 7:53 pm
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    cough cough brains cough cough homer and bart cough cough retards

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  • April 28, 2019 at 12:16 am
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    That guy's accent is so thick

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  • April 29, 2019 at 3:14 am
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    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.

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  • April 29, 2019 at 6:52 am
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    Inside of a sphere? Where c is closer to the 'equator'

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  • April 29, 2019 at 6:53 pm
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    What c squared equals a squared plus b squared minus 2 times a times b times cosine of opposite angle of c?

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  • April 30, 2019 at 7:07 pm
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    The solution is sqrt(1/e) + sqrt(1/e) = 2 × sqrt(1/e) or (1 – sqrt(1/e))

    The number approx 0.367…

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  • May 1, 2019 at 3:44 am
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    The Pythagorean Theorem but it's the opposite day

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  • May 1, 2019 at 7:49 pm
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    "european improves animation with numbers"

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  • May 2, 2019 at 2:23 am
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    An isosceles triangle can be a right triangle, though.

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  • May 4, 2019 at 2:11 am
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    81sqroot+256sqroot=625sqroot

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  • May 9, 2019 at 4:01 am
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    Inverted sphere?

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  • May 10, 2019 at 1:04 am
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    Alright recommended videos. You win this one.

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  • May 10, 2019 at 6:13 am
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    NEEEEEEEEEEERD!

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  • May 11, 2019 at 7:25 am
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    5:49 But c is a little bit longer than a and b put together. How long is 2Sqr(a)Sqr(b)?

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  • May 13, 2019 at 7:50 am
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    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

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  • May 14, 2019 at 4:02 am
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    16a^2=2a^2+2a^2cos(theta)
    2cos(theta)=14
    cos(theta)=7
    That's why such a triangle doesn't exist

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  • May 19, 2019 at 11:38 pm
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    Can we turn the background black? Or blue? Kills my eyes at night

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  • May 29, 2019 at 12:53 am
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    obvious answer: it's the pythagorean theorem.

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  • May 31, 2019 at 1:07 pm
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    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.

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  • June 1, 2019 at 5:15 am
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    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."

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  • June 4, 2019 at 2:26 pm
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    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.

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  • June 5, 2019 at 5:11 am
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    Homer was quoting the scar crow after he got his deploma at the end of the Wizard of Oz.

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  • June 9, 2019 at 8:19 am
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    Square root of any side of an equilateral triangle is equal to the square root of any of the two remaining sides. 🙂

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  • June 10, 2019 at 4:26 am
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    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

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  • June 12, 2019 at 7:40 pm
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    A right triangle CAN still also be isociluse

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  • June 12, 2019 at 7:43 pm
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    It works if it's an equilateral triangle with a side length of 1

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  • June 15, 2019 at 10:05 pm
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    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!

    Reply
  • June 16, 2019 at 11:36 pm
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    Cool Video!

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  • June 20, 2019 at 2:10 am
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    I know it was refraction at first, its the second part of the question thats hard to answer.

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  • June 21, 2019 at 5:32 am
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    A 2x longer, not 4x

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  • June 21, 2019 at 4:06 pm
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    Danil Dmitriev, спасибо

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  • June 22, 2019 at 6:36 am
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    Because the people that do cartoons studied graphic desing not math.

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  • June 22, 2019 at 10:58 pm
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    @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! 🙂

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  • June 27, 2019 at 4:29 am
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    Did anyone mention Simpson's rule on the show?

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  • June 27, 2019 at 4:33 am
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    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.

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  • July 2, 2019 at 7:54 pm
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    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.

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  • July 3, 2019 at 6:03 am
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    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

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  • July 4, 2019 at 10:34 pm
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    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")

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  • July 5, 2019 at 8:39 am
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    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.

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  • July 5, 2019 at 11:27 am
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    His laugh is adorable. Love it!))

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  • July 6, 2019 at 9:58 am
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    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.

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  • July 8, 2019 at 6:47 am
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    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.

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  • July 8, 2019 at 5:09 pm
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    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.

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  • July 9, 2019 at 7:27 am
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    Maybe in a pseudo sphere

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  • July 9, 2019 at 9:29 am
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    √a + √b = √c for a right triangle isn’t incorrect if a b and c are define to al be of the fourth root.

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  • July 10, 2019 at 3:12 am
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    Your diagram looks like bart's head.

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  • July 11, 2019 at 2:25 pm
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    "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."

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  • July 13, 2019 at 7:11 am
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    There are 2 complex solutions to that equation if you try to find the cosine of the equal angles which is 2.

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  • July 14, 2019 at 7:51 pm
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    @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)

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  • July 14, 2019 at 9:38 pm
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    to be fair: the scarecrow got a perfectly working brain. Probably could run for us president with it

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  • July 14, 2019 at 11:22 pm
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    [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 !

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  • July 15, 2019 at 2:03 pm
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    Reminds me of the Optimist's Theorem: √(a^2 +b^2) =(a +b).

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  • July 16, 2019 at 6:36 am
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    Simpson’s have many times shown controversial predictions and statements

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

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  • July 19, 2019 at 4:32 am
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    It would be fun if it worked on a donut surface… 😉

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  • July 21, 2019 at 9:18 pm
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    I don't think topology would allow that for any spce, as weird as it might be.

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  • August 1, 2019 at 2:42 am
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    Español: el teorema de homer
    Demas hispanohablantes: https://bit.ly/2YAdm8u (Es una imagen, abrelo xd)

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  • August 1, 2019 at 2:39 pm
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    A rt angled triangle with the sides opposite and adjacent being equal in length – is also an Isosceles triangle.

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  • August 3, 2019 at 3:57 am
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    aww i was hoping you'd immediately cover the case of hyperbolic topology =} i dont understand it that well

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  • August 3, 2019 at 10:36 pm
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    I think Futurama has more Math in it then the Simpsons one of its creators holds a PhD in Math & Physics.

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  • August 7, 2019 at 8:58 am
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    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

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  • August 9, 2019 at 7:56 pm
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    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” !

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  • August 10, 2019 at 3:34 am
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    El título me salía en español, me siento engañado

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  • August 14, 2019 at 10:28 am
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    It is maths. The word is plural, not singular.

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  • August 21, 2019 at 12:25 pm
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    3:01 Is he sure he's not him?? They look very similar

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  • August 22, 2019 at 3:49 pm
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    There is a right triangle that is an isosceles triangle, so the argument is correct.

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  • August 26, 2019 at 6:53 pm
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    @ 4:20 there is something green written on his hand.

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  • August 27, 2019 at 1:41 am
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    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)

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  • August 27, 2019 at 8:47 am
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    In a complex plane?

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  • August 27, 2019 at 8:53 pm
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    mhh…. I was waiting for the proof that √a + √b = √c could not be solved for any nonzero whole numbers. Or can it?

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  • August 28, 2019 at 12:49 am
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    I have discovered a truly marvellous proof of homer’s theorem, however this comment box is too small to contain it.

    Reply
  • August 29, 2019 at 4:00 am
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    It should work on a toroidal. I have imagined the triangle embracing the lap

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  • August 29, 2019 at 6:26 am
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    4:19 A handful of notes.

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  • August 29, 2019 at 9:00 pm
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    On a sphere when: c > π·r

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  • August 30, 2019 at 3:07 pm
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    Please look at EPISODE 9 from 12 -TEMPORATED WHERE HOMER GETS INTELLIGENT! Aah!
    😉✌👋

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  • August 30, 2019 at 9:42 pm
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    What about when dealing with side lengths all less than 1?

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  • August 31, 2019 at 1:41 am
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    if you collapse b to zero, in the limit the second case works. the first case only works in a moebius strip.

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  • September 2, 2019 at 6:50 am
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    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

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  • September 5, 2019 at 4:45 am
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    a+b=<c could work if the plane had 3 dimensions and you looked at it at an angle. ie, a projection.

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  • September 11, 2019 at 9:11 pm
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    If c is nearly as big as the circumference of the sphere you could make a triangle where (a+b)<c.

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  • September 12, 2019 at 8:24 pm
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    heheehe for all this the solution is a dorito's chip …if you cannot see it lmao

    Reply

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