Math in the Simpsons: Homer's theorem
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- เผยแพร่เมื่อ 30 ก.ย. 2024
- After putting on some glasses he found in a toilet Homer feels very smart and declares: "The sum of the square root of any two sides of an iscosceles triangle is equal to the square root of the remaining side." Well, sounds like Pythagoras theorem but it's not. The Mathologer sets out to track down this mystery theorem to its lair and dissects the hell out of it.
Enjoy :)
I was more worried about him putting on those toilet glasses without washing them first.
I like to think they have him go to the sink to put them on as a tease. "Oh good, he's at least going to rinse them." Then you remember this is the man who once was craving beer so much he licked the dirt under the bleachers at a baseball stadium.
Cartoon germs don't cause infections unless the plot calls for it.
Ross Plavsic wow, you look really similar to him
I love your videos.
I won't even touch it.
The video no one really ever needed but it's always good to educate the masses.
You didn't account for Non-Euclidean Geometry!
Ia Cthulhu Fhtagn!
he did tho, spherical geometry ain't euclidian ya cook!
????????????
en.wikipedia.org/wiki/Spherical_geometry#Relation_to_Euclid%27s_postulates
I completely forgot that line from WoO! It is kinda funny how in the movie they act like his diploma gave him magic smart guy powers and he *immediately* says something mathematically incorrect
If you bisect the hypotenuse of a right triangle and move out equidistantly on either side, the product of the (x,y) coordinates that subtend the two points - that is the areas of the rectangles that these two points define, will be equal. Obvious by inspection in a 45/45/90, but less so if the right triangle is scalene. BTW this is one of my theorems.
Well known rule that the shortest distance between two point is a straight line.
So if Side C is that line, it the shortest distance between Angle a and Angle b Side A and Side B will always be at an angle of each of or they be considered the same side there for the sum of Side A and Side B will always be longer than Side C If not you have divide the rule.
I never would have understood this as a missing link joke before now lol.
Why is he asking the camera man to help him do the algebra?
Is the cameraman a scarecrow?
It represents us
to give the viewers (us) time to process the algebra naturally and keep up with the work.
@Mathologer One way you could have a triangle with the long side greater than the sum of the two short sides is if the triangle was on a sphere and the long side was greater than half the circumference of the sphere. At that point it wouldn't look much like a triangle but it technically is possible to make Homer's Triangle.
You know , perhaps when he said an isosolece triangle he meant both an isosolece and right. In other words , a 45 45 90 degree triangle . It is both isosolece and right , which would work to SOME extent , maybe
WHAT WAS HIS LOGIC? I'M HERE FOR THAT KIND OF MATH
2:57 great roasting
A rt angled triangle with the sides opposite and adjacent being equal in length - is also an Isosceles triangle.
And if each of the sides opposite and adjacent are designated as sq root of 1, then the base of the isosceles triangle (ie the hypotenuse) will be Root2.
I think a triangle with c > a+b can exist if we make the c side longer then the half of the circumference of the sphere (and the other two sides shorter). Otherwise it can works on a cylinder or if we use the hole of a torus I think.
if I am wrong please explain me why, I would be intersted. (and sorry for grammar, I am not english)
the reason why a+b > c is because a and b will always have to cover the same length c does plus a bit more since they are diagonal
I am in 8th grade, I don't have the knowledge of you guys, but according to my calcualtions,
the equation works if the triangle is a right isosecles one.
your brain is reaching levels previously thought to be unatainable, keep going young one, you are destined for greatness
Bingo!
Woahhhh so the simpsons was just referencing the wizard of oz. that’s a deep joke
shottysteve and the wizard of oz was just the result of the writers
Wow only 2 likes on a verified comment
make a new video already
make a new video already
make a new video already
I share this video with my students. Veeery goooood!!
Estava pensando exatamente isso. Quando eu estava no ensino fundamental/médio não conseguia visualizar as equações dessa forma, era tudo muito abstrato, depois desse vídeo consegui compreender algumas coisas da época da escola.
Spanish spanish Spanish spanish, whatever the dude above me said.
@@ADrunkCrayfish It´s portuguese, dude.
@@ADrunkCrayfish that ain’t Spanish
@@irioncampello6055 Well, I certainly em read it in Spanish, and am portugueses speaking! 😂
Scarecrow doesn't get a brain, he just get a diploma.I think that the reason.
XD
He said he got a brain :) 2:55
@@just_is He has a brain, he had one all along, but he didn't get a new brain :-)
Scarecrow is just like every other person with a college diploma :)
even back then they knew how useless college was.
@@aidenaune7008 college in America is a class gate to limit upward mobility.
Oh man, I got that Homer's line was an homage to Wizard of Oz, and I could get that Homer got the Pythagorean theorem wrong, but I never noticed that the original line in Wizard of Oz was wrong!
But Scarecrow is a Doctor of Thinkology!
I know this is a year old...
One of main themes in Oz is that magic can't solve your problems. The wizard actually doesn't do anything in the world (allegory for false promises of politicians) and the work is left to the outsider Dorothy.
Scarecrow thinks he's been fixed, but he was already "fixed," he just didn't know it.
@fangere
That's beautiful.
Thank you.
🥰
@@MattMcIrvin so scarecrow works in the liberal arts?
I don't remember noticing that either! The lines go by so quickly it's hard to notice exactly which words they are using or have time to think about it!
Are you just pointing to a white wall and memorizing what to say?
He's holding a remote so I imagine that when he looks towards the camera, he's looking at a screen with a sort of slideshow on it
There's a projector that projects the slides onto the wall. The clean slides are superimposed in post.
@@itzmistz no, it's not. it's a green screen, he has a monitor to the side where he looks at a teleprompter or notes or a slideshow, and the edit is placed over later. no projector
@@PhazedAU You wouldn't be able to see shadow on the 'green screen'. Also look at 1:37, the text is clearly on his hand from the projector
To be honest, it could be a combination of both. I do see a bit of green
It should be called the placebo theorem as all the instances we see it are the individuals thinking they're smarter.
Well one of them was practicing lines for the scarecrow, so technically it's right there.
Aaron Reamer
That's not what a placebo is.
@@ImDemonAlchemist The definition of a placebo is "A medicine or procedure prescribed for the psychological benefit to the patient rather than for any physiological effect."
You could say that homer receiving the glasses or the scarecrow receiving his "brain" making them think they are smarter when in fact they are not as a placebo effect.
This guy is a perfect example of the Dunning Kruger effect...
@@awulfy9052 Exactly. Its the Dunning Kruger effect, not a placebo effect.
Minkowski metric in spacetime satisfies a reverse triangle inequality
Can I bear your children?
@@csaw1270 Yeah no prob LOL
@@obi6822 I'm a dude so I'd have to father ur children actually which would defeat the purpose
@@csaw1270 I assumed so. I am a dude too btw hahaha
@@obi6822 if I was a woman I'd bear your children. How bout that?
This triangles could exist in a cilinder
Vicio ONE MORE TIME!!!! Better the inside of a sphere
These* :v
I suppose if you take a cylinder at least 4 but less than 6 units in circumference and wrap the big side around and join it with the two shorter sides. I'd hesitate to call it a triangle though. It would be more like a letter C with the gap joined by a little v at right angles.
What I thought
@@misael8200 you're not going to talk about the cylinder?
Hold on: If b=0, then we have a line. Then, solve for a using the first equation, and you get (a)^(1/2) = - a^(1/2), so a=0. Thus, you are left with a point. That's the joke! They have a point! :)
This is THE answer.
Sorry, I don't speak Egyptian. Can you translate?
LOOOL
Hold on, I don't think it'll work like that. We got b=0 for the second equation, so we can't use that in the first equation. These are not a set of equations, rather a matter of either/or . Also yeah ik this is meant as a joke lol :-)
This line is also referenced in an episode of Hey Arnold, where Arnold’s grandpa goes back to elementary school to get his grade school diploma. Funny thing is Dan Castellaneta (who voices Homer) also voiced Arnold’s grandpa, whom recites this line to the principal in order to secure his diploma.
Maths are interesting to begin with but immediately becomes ten times more enjoyable when explained by someone with a German accent.
He is not German bitchface
@@Л.С.Мото Austrian? Swiss?
Right here Right now yes, he is German. If you don’t think so, just google him “Burkard Polster”
@@Л.С.Мото wth he is are u sutpid
Actually, Homer's mistake was.....
…he didn't wash the glasses before putting them on his face.
Copied :(
Pink eye time
They were already washed, just not with water from a preferred source
David^2 - S^2 = Cohen^2 gives us a hint: the "D" from David stands for Donut, the S stands for Sign and the C stands for Colossal donut. When homer points at the colossal donut, we can see all of these 3 points (donut, sign, colosal donut) in one frame. If we connect these 3 points we get a triangle where a is the height of the sign including the colosal donut. You can also measure the angle of homers arms (alpha): 10, and the credits give us the number 24m as the length of b. We can now calculate the length of the hypothenose c: 24/cos(10) which is 24.3. Now we can calculate a: sin(10)*24.8 which is about ~4m. This means that the man holding the colosal donut plus the colosal donut is 4 meters high. They are about the same size so we can divide by 2 to get the size of the colosal donut: 2 meters!!!
SinOfficial this is like the kind of comment i sometimes make but this is way better! Good job at figuring that out!!
I accept this as fact
Why can’t I be smart like this. DOH!!
if you had used tau instead of pi in your calculation, you wouldn't have had to divide by 2 at the end.
@@prezadent1 homygod
8:13 one of the co-producer's name is "David² + S² = Cohen²"
well spotted!
Nice!
Haha I made it harder than it was and I thought it was the right triangle made to scale the small donut to the colossal donut XD Good job!
it was shown at 8:39 anyway
That actually says '2+' on each power, which is actually probably better read as a contradiction of Fermat's last theorem, and if I remember my Simpsons correctly, is not the last such contradiction in the episode :) check the equations in the background when Homer is in the 3rd dimension...
remember, he's got a crayon stuck in his brain.
What about a triangle on the surface of... a doughnut?
+HerraTohtori Well, with more complex surfaces you first have to make up your mind what exactly you mean by a triangle. I've left a few comments earlier on in which I talk about this. Maybe have a look :)
I was thinking that would make sense considering Homer's favorite junk food! As for the math to prove it, I'll leave that to folks with more time and math training than me. If true, maybe Wizard of Oz screenplay writers (or Baum himself, if those exact words are found in the book) had donuts on the mind and/or knew something about tori.
it is a torus
They already did it!
Season 10, Episode 22 "They saved Lisa's brain"
Stephen Hawking: "Your theory of a donut-shaped universe is intriguing, Homer. I may have to steal it"
(Dun dun duuuunn)
Can't it be done on a torus?
He even tested the Scarecrow Theorem in non-Euclidean geometry! I didn’t see that coming.
Any Lorenz geometry model usually works without triangle inequalities. Not sure now, but maybe homer's theorem holds true for minkowski space? Where triangle inequality is reversed?
Good idea :)
Human Effigy no Minkowski's, but it works on a sphere in Minkowski space
i didn't get a word of this, but Mathologer replied means this wasn't bs
so liked the comment
The simple fact that this guy so sincerely loves both math and the Simpsons makes me like him immensely.
OMG Crystal math lmao
First comment on a post from 2016 in 2020
Second
@@protat0 no one cares
Every adhd medication is similar to meth
A man in the lightmode void talks about the mistakes Homer Simpson makes while looking at an omnipresent context and visual providing object that reacts to both his words and the content it showed previously.
i'd say it's a well planned powerpoint presentation
I just want to say that I really enjoy this channel. It's difficult to find interesting videos about cool bits of mathematics, and so far I have found 2 channels that deliver this: numberphile and mathologer. Keep doing what you're doing!
I totaly agree!!!
You're missing 3blue1brown, especially if you're already somewhat advanced in your maths education. But even if you're not, there's plenty of cool stuff on that channel too, definetely check it out.
(i know the comment is old af, but if you haven't seen it since then, GO FUCKING DO IT :p)
@@FelipeV3444 actually i was going to comment this... Lol😂
That part of Wizard of Oz always (well at least after middle school) pissed me off .
+DrRawley I think the point of it was as an in-joke: the Wizard never gave nothing to the Tin Man that he didn't already have, and all.
Qermaq I know :( That part pissed me off too. It's all a lie.
+DrRawley But WE know it is. That makes us richer. :)
The wizard was a dick.
+DrRawley Seen Wicked?
Realized the same, but I though it was a translation error. Didn't know there was a whole video about.
TH-cam always surprise me.
8:12 found pythagorus in the credits
David^2 S^2 = Cohen^2
It works on a sphere when you ignore the any sides part. You can create a triangle were two of the sides equal a quarter of the circumference of the sphere and the other one spans around the equator. The angels between the equator line and the other two are always 90°, therefor the triangle is iscosceles. The third side can now vary from 0 to the circumference of the sphere. So if you subtract the other two sides (which equal half of the circumference) you still got the possibility to have half of the circumference left. Since in this example a equals b 2*(square root of a * square root b) equals 4*a. Since a equals a quarter of the circumference you get the solution when c spans the whole circumference. It doesn't look like a triangle but technically it is a triangle on a sphere I guess.
Frame by frame from 8:14, you quickly get 3 and 4 dots on the donuts, 5 teeths in Homer’s mouth... That’s the first pythagorean triple!
+The Einhaender I’m afraid that’s it... 8:20 He said "it’s a tough one" and "there is a *hint* in the credit". Then at 8:38, they give the credit hint. I can’t believe the solution is this obvious. If it was all, they would say, the *solution* is in the credit, or something a bit more allusive I guess... David S Cohen is the math guy he must have done something clever in the sequence, not just adding a few squares in the credit... ;-)
My comment was totally desperate, I know it can’t be about the dots on the donuts. I searched for triangles that could have some obvious ratios, I couldn’t find any right triangle! Or maybe some circle with a crossed diameter, no chance... I’m afraid I’ll just be disappointed in the end. In ... Anyways, the show is great.
+boumbh The funny thing is that DAVID^24+S^24=COHEN^24 is not possible according to Fermat's last theorem
+Aishwarye Chauhan Actually, it just says that if it is true, then DAVID, S and COHEN cannot all be positive integers.
Fennec Besixdouze Oh, there is a corollary or something, right? I was thinking on Fermat's original proposition, and I forgot about generalizations.
leonardo21101996 exactly. I missed the whole been integer part haha
On a sphere, it is kind of possible to have a+b
In spherical geometry opposite points on the sphere are considered equivalent: this is because it changes the 5th postulate to say that parallel lines do not exist: lines can only be maximum circles (circles made by a place cutting the center of the sphere). All lines are perpendicular and cross at ONE point: so they consider the opposite points as one single point. So some of those points on your bigger side are part of the original triangle and the others are excedent like a side prolonged even ending on the same points. The distance in Riemannian geometry is given by the SMALLER maximum circle because a metric can not be a multivalued function and the metric by definition must obey the triangular inequality (or the hell will go loose and several contradictions arise because the metric should capture the intuitive notion of distance as being additive, and being symmetrical (in a loose sense that I am too lazy to explain). So your construction is not a triangle is a triangle with line segments added (my explanation is a little convoluted because I am lazy, maybe later I explain better).
@@agranero6 no they aren't
There are examples in which an instance of that formula, sqrt(s)=sqrt(x)+sqrt(y) may be found.
The triangle inequality is reversed in Minkowski space, so that's a candidate.
Secondly, it might be possible to find instances of that on some surfaces, such as a variant of the pseudosphere or some other surface of revolution of some cusp-containing curve.
Finally, something similar to it can be found in particular Lp spaces. For example, a space with a norm |s|^p = |x|^p + |y|^p will have something akin to the required formula for, say, p=1/2
What I find very intriguing about the last option is that circles, when drawn on a euclidean plane, will look like Lamé curves (with the power parameter being 1/2).
In short it can be done in spaces with a quasi-norm.
Definitely the best answer so far :) (Minkowski space has been suggested before)
I don't understand but this sound really brilliant. What kind of math this is?
Goldmos1
It's geometry and vector spaces.
Late to the party, I know. But my point is that sqrt(a) has TWO values.
sqrt(b) + sqrt(a) = sqrt(a) might not work, but sqrt(b) - sqrt(a) = sqrt(a) could easily be true, as well as -sqrt(b) + sqrt(a) = sqrt(a)
@@Goldmos1 topology I believe, I'm taking my first course in it now (MATH 525). I'm in my final year as an undergraduate and the stuff in the post seemed like stuff I could probably start to grasp. And I'm in North America, you can learn any mathenatics you want. You just have to be passionate and eyeballs deep in student loans! (The later may be optional if your really gifted or driven, but scholarships are few and self study is difficult)
SCARECROW THEOREM SHOWN TO BE CORRECT!
After the Scarecrow got his brains, this is what he actually said:
"There is an inverse stereographic projection of an isosceles triangle onto a 3-D surface, such that the curve length of each of any two sides is equal to 1, and the 3-D surface can also be constructed such that the remaining side would have a projected curve length of 4. Thus, considering the projected sides...
...The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side."
Unfortunately, most of the Scarecrow's mathematical statement ended up on the cutting room floor. All that is left is the abridged and inaccurate version in the movie. Hollywood had no appreciation of the Scarecrow's mathematical genius.
I don't know about math, but in physics, if you use a spacetime graph, the hypotenuse is the shortest side
+Jasper Tan thats a minkowski space (split-complex plane), but i don't think it works there either, not for all triangles at least.....
+John Galmann It does as long as all the lines are timeline - and that gives rise to the so-called twin "paradox" (not a paradox at all, of course, just the result of the triangle inequality in a Minkowski space).
So when Homer said that, he was obviously referring to lines in Minowski spacetime.
Home Simpson secret genius confirmed.
Jasper Tan citation needed... That silly formula for the Minkowski metric doesn't make much mathematical sense, especially considering that the distance between two distinct simultaneous events is an imaginary number(?!)... Even assuming that is the case, imaginary numbers aren't comparable, so the hypotenuse is neither shorter nor longer. :-\
@@irrelevant_noob Of course you can order imaginary numbers; you can't order complex numbers.
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.
David²+S²=Cohen²
I think Futurama has more Math in it then the Simpsons one of its creators holds a PhD in Math & Physics.
Omg that poor scare crow xD
He makes us all look bad.
It is quite wrong ... but ... it can get even wronger 🤣🤣🤣
Awesome job providing the clips, ALL of them, including the Scarecrow.
3:05 He got a brain just not a very good one.
If the triangle is inside of the sphere, the two shortest lines can split from the longest line right before it makes the full radios. it would be a weird shape. but it would have three corners and it would give the two short sides a opportunity to be infinitely shorter then the longest line. Also works for the outside of the triangle ofcourse :)
not radios, But diameter.
The Wizard of Oz's scarecrow got Homer Simpson's brain!
... or the scarecrow is Homer Simpson's REAL dad!
@@SeanJTharpe He's nothing but hay and cloth. I doubt he's got genitals.
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....
Not sure if I'm being an idiot and I would like more insight on this but wouldn't that Mercator projection make a hemisphere with a triangle missing instead of a triangle since the inside angles would exceed 180 degrees
7:00 The answer is *never* on any Riemannian manifold ... if "length" is defined as *geodesic distance* ... because the geodesic is the *shortest distance* between two points, which forces the triangle inequality. Now, on a *pseudo-Riemannian* manifold (even flat, like Minkowski space), that's another story.
This leads naturally to a question for you: do the flight distances of New York, Miami, Chicago and Houston fit in *any* Euclidean geometry, if they are treated as straight lines? If not, then what's the minimum curvature they must have before they do? What about other sets of 4 cities on the Earth, like London, Tokyo, New York and Johannesburg? Which geometries will 4 cities fit on, as a function of how much curvature their flight paths are endowed with? (Yes, some cases require a 2+1 dimensional Minkowski Geometry).
What about 5 or 6 cities? And since the Earth is *not* a sphere, what happens if you try to fit 6 cities, as a function of the curvature you give all the flight paths, assuming they're all given the same curvature? How much information can be said about the dimensions of the Earth - as well as the cities' *latitudes and relative longitudes* - on the assumption that the 6 cities fit on a ellipsoid? Try it with { New York, Miami, Chicago, Houston, Los Angeles, Seattle}, as well as {London, New York, Tokyo, Johannesburg, Melbourne, Rio de Janeiro}.
Sorry - geodesics are NOT necessarily the shortest routes between any two points. Geodesics are only LOCALLY the shortest routes between two oints.
Love these. My favourite bit of Simpsons math was when Homer had to count himself to be sure he was just one man.
I wonder if the point was that the scare crow didn't really get a brain. He just had to think he did. The líon just had to think he had courage and the tin man had to think he got a heart. Which is kind of an interesting angle from when I was a kid and I literally thought they had somehow actually received these things.
There is no metric space where this equality could happen. In particular it is not true for any space with metric (Riemannian manifold: en.wikipedia.org/wiki/Riemannian_manifold), the sphere included. In such a strange world we would have a distance function which is does not satisfy the triangular inequality ...
it's been a long time since I used any high level of math. mostly basic stuff, Pythagorean theorem always comes in handy, and geometry in general. I do grow increasingly fascinated with Eratosthenes. This guy was simply amazing. Kind of sad, put in all those endless hours of head splitting work, worry, study, panic, study more, obsess, and in the end I have to periodically give myself math test so I don't forget all of it. everything today is charts, computers, and more charts. I remember i started my job and could figure everything with mobil calculator, pencil, and paper. Co-workers were jealous I believe and said why figure it out like that it's in the tables. One professor I had said - I feel sorry for you if technology ever crashes. At The time I didn't care The exams were so damn long and hard that without a calculator I would have had a nervous breakdown trying to crunch it all before I ran out of time. Now I understand though. The most important stuff you will need in life is college algebra and geometry maybe some trig but probably not. However when you have that knowledge it feels good. In a job interview I got asked a math problem and immediately pointed out the flaw in the question and offered a math solution to solve it. The other mathlete in the room laughed and of course no job for me. However, it felt damn good.
That dude is super chill and the math looked like legit math so I guess this added value to my day
"pah, the way people act around here, you'd think the roads were paved with gold"
"they are"
There's the time homer solves fermat's last theorem. But they used an edge case where the answer is incorrect in decimals that a regular calculator doesn't show
The homer theorem would work in hyperbolic space in some cases i think
+Carol Vitez Yeah that's what I was speculating.
+Carol Vitez wouldn't it work on a torus?
+dalmation black
yes it would I think :)
Your theory of a Donut shaped universe intrigues me.
@techtrashing: Play some old Super Nintendo RPGs that feature a world map. The world map will usually loop from "west" to "east" and "south" to "north", thus forming a donut shaped world.
he was quoting the mistake in the wizard of oz
It could work with complex numbers where i*i=-1, then:
a*i + b*i +2sqrt(a*b*i*i) = a*i + b*i - 2sqrt(a*b) = c*i
might lead to some solutions.
p.s. oh... its 5 years old - saw 5th of september and didnt noticed the year :D
If I had learned math this way in school, I think I would less suck at it today. Still I am learning things here.
It is maths. The word is plural, not singular.
"Homer knows isosceles triangles? It's ridiculous." Hahaha. :)
If you play with the first 20 integers for √a+√b=√c you get that a+b can be 32.00%, 37.50%, 44.44%*, 48.00%, 48.98%* or 50.00% of c but never more. The best, ie 50% is where a=b, so a+b=½c.
[Within the arbitrary limit I set] The squares 1, 4, 9 & 16 have the most integer solutions, 4 each, and the odd primes have the fewest, one only where a=b≡p because the square root of any prime is irrational.
* not exactly, the others are precise.
Isn’t the gag that the Scarecrow got a diploma, not an actual brain?
Someone's putting quite a lot of faith in the writers
Hmmm...
What is "distance" mean? And how to "measure" it if your "eyes" (is/are) "different"?
I think it's "peenokia'
Simon Singh has a great book on the Mathematics in the Simpson's. Many of the writers held STEM degrees.
Maybe intended, maybe sheer luck, but the first frozen scene: 1 mirror + 2 sinks = 3 stalls (left) + 5 stalls (right) = 8 tiles in lenght
I think I have an easier proof for the isocele triangles that 2*sqrt(a) =/= sqrt(b).
You can construct an other isoceles triangle with the equal sides which are still a and the remaining size which would be b' =/= b.
Assuming the theorem mentionned is true, you have that sqrt(a) = sqrt( b )/2 = sqrt( b' )/2 which is a contradiction.
+nico.og Cool :)
For triangle inequality to fail, the space would not be a metric space. Minkowski space has pseudo Euclidean metric so it might work there.
Or, stretch the definition of triangle so it does not have to be three points with the shortest paths between them, but any geodesic is allowed. Then there are such triangles on the sphere, by taking the greater arc instead of the lesser arc for the longest side.
2:59 Is it normal that i see some similarities with the mathloger ?
He got the brain, went to Australia and became matematician.
In one of the episodes in which Homer tried to become an inventor there is a reference to Ferma's last theorem :).
+Jelle (NL) Ah, yes, that's a nice one. There are actually two occurrences of "counterexamples" to Fermat's last theorem in the Simpsons. The one you mention is the second one. The first one pops up in Homer^3 (Homer cubed) where Homer stumbles into a 3d world. Very neat stuff. There is also one mention of Fermat's little theorem in the Futurama Simpsons crossover episode.
+Mathologer keep the counterexamples in quotation marks. As per the numberphile video those are only close to a solution, not exact. (even the parity of the sum is wrong).
P.S. just to make sure no one thanks Ferma's last theorem is debunked.
A world where a+b can be less than c can be gotten by taking that sphere diagram of yours, and having c go the LONG way around the circle instead of the short way. Boom, a+b
I know this is old but I'm going to take a crack at these Pythagorean clips.
In the first clip, David S. Cohen's name is written as "David^2+S.^2 = Cohen^2", quite clever ;)
Of course, the second time around, A^2+B^2 = C^2 is just on the "MATH BOOK"
I know this is a dumb question...I guess I'm just not nerdy enough, but I don't get the joke. how is "David squared plus S squared = Cohen squared" clever? Is there some hidden meaning? Is there some sort of language wordplay thing going on there? I understand the pythagorean theorem, I understand the reference, but I don't get the joke.
+FeMaiden Maybe it's clever because no one ever looks at the credits so it was at least harder to find than the other example.
oh yeah, I looked back and I see the joke...it was just wordplay like on the halloween episodes they do that with the credits like "James Hell Brooks" instead of "James L Brooks"
I just thought maybe it was some sort of like...higher mathematics joke like a reference to a famous equation or something.
I did the calculations thinking that David^2+S.^2 = Cohen^2 would correlate numerically, if, for example, each letter associated with a number value (A=1, B=2, C=3)... but I didn't find anything. Someone can check my math, but I got DAVID (4+1+22+9+14)=40^2= 1400 Plus S (19)=19^2=361, so together 1961 equals COHEN (3+15+8+5+14)=45^2=2025. So, all together, 1961=2025 which obviously doesn't add up.
Tim Westchester 1400+361=1761, not 1961.
I don't understand why you think Homer is wrong, it's a perfectly cromulent theorem
The Pythagorean Theorem but it's the opposite day
Tipico, entras a un video que aparentemente está en español y nada más entrar ves que youtube te engaño y la lengua madre de la que parte el video es el ingles. . .
Un gran sabio dijo una vez "Estoy feliz y enojado".
Videos like this make me feel dumb, I wish I was smarter....
Just keep watching these sort of videos and you'll understand more and more as time goes by :)
Did it work yet?
Bart's "vitamins" include 'Crystal Math' and 'Brozac'
His laugh is adorable. Love it!))
I think you missed the joke. The scarecrow says that after he got “the degree”…he always had a brain.
Wow, never knew that was a Wizard of Oz reference lol
I knew it was a reference to the Wizard of Oz but never noticed it was word for word the same line. I misremembered it as the Scarecrow getting it right in the movie and the joke being homer getting it wrong
What if there was a isocles right angle triangle with two equal sides? You'd be right on one occasion.
So a 45-45-90 triangle. :P
They do know The Simpsons referenced The Wizard of Oz right?
When your literature teacher interprets a passage in a book
If we modify it just a little bit, so it says: c = sqrt(a) + sqrt(b) then some triangles do satisfy this, like a = 1, b= 2, c = 1+sqrt(2), but this is no longer Homer's triangle. Though, who knows. maybe the Scarecrow-Simpson triangle needs complex dimensions. I haven't tried that. :D
I feel like most people won't realize that was a Wizard of Oz reference... Myself included.
You can't violate the triangle inequality, a+b>c, with some weird surface because no matter what surface and metric you're using, by definition the metric has to satisfy the triangle inequality. The only way is if you choose the sides of the triangle to be something other than geodesics (shortest paths), in which case you don't really have a triangle, just some 3 vertex shape.
I didn't say straight line, I said geodesic, which exist in any space, not just the plane.
The only time this equation works is if all the terms are zero. So he has a point.
I thought any metric that is constructed must still obey the triangle inequality. Even if it a + b = c.
Definitely, if you are in a "metric space" the triangle inequality has to be satisfied. But there are weird "reasonable" spaces that are not metric spaces. There have been a few suggestions in earlier comments :)
A cone shape would work for the triangle that the sum of two of the sides are smaller than the other side?
When I was riding in an elevator with a colleague, I asked him what he taught. He said "Math." He asked me what I taught and I said "Communications." He smugly replied "That doesn't count." He explained that math was the only subject that was worthwhile.
Don't get too full of yourselves math people.
Lol, that doesn’t COUNT😂
But math is used more than communication. For money, daily life, investigations. Yes, communication is used a lot, but math is more common
@@hanchrisyt4school995 Communication is used for way more than math. Math is pretty useless if you can't communicate.
"Math is the only subject that counts" he communicated to you.