Math in the Simpsons: Homer's theorem
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- čas přidán 3. 09. 2015
- 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.
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
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!
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.
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
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.
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! 😂
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?
Minkowski metric in spacetime satisfies a reverse triangle inequality
Can I bear your children?
@@calvinsawyer1961 Yeah no prob LOL
@@obi6822 I'm a dude so I'd have to father ur children actually which would defeat the purpose
@@calvinsawyer1961 I assumed so. I am a dude too btw hahaha
@@obi6822 if I was a woman I'd bear your children. How bout that?
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
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
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 :-)
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
@@user-sj2vg8hb5q Austrian? Swiss?
Right here Right now yes, he is German. If you don’t think so, just google him “Burkard Polster”
@@user-sj2vg8hb5q wth he is are u sutpid
remember, he's got a crayon stuck in his brain.
The simple fact that this guy so sincerely loves both math and the Simpsons makes me like him immensely.
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...
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 :)
+Mathologer A closed curve made of 3 geodesics. Yes it can be done on a torus.
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)
He even tested the Scarecrow Theorem in non-Euclidean geometry! I didn’t see that coming.
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.
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
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😂
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
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)
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.
Awesome job providing the clips, ALL of them, including the Scarecrow.
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?
8:12 found pythagorus in the credits
David^2 S^2 = Cohen^2
If I remember correctly if you know the length of two sides of any triangle (a and b) the third side (c) has to be:
a-b < c
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.
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
Love these. My favourite bit of Simpsons math was when Homer had to count himself to be sure he was just one man.
I think Futurama has more Math in it then the Simpsons one of its creators holds a PhD in Math & Physics.
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
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
David²+S²=Cohen²
Realized the same, but I though it was a translation error. Didn't know there was a whole video about.
CZcams always surprise me.
On a sphere you can get it so a+b
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.
"pah, the way people act around here, you'd think the roads were paved with gold"
"they are"
Simon Singh has a great book on the Mathematics in the Simpson's. Many of the writers held STEM degrees.
Omg that poor scare crow xD
He makes us all look bad.
That dude is super chill and the math looked like legit math so I guess this added value to my day
Subscribed! relating math to the Simpsons/futurama is a great motivator to get me through my homework! Thank you
you can make a triangle where a+b
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.
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.
This is such a great channel.
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.
I like that you’re talking to the camera guy, its fun having you two bounce math off each other instead of just one guy talking into the void
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
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
Ive never seen your channel but i found this very intriguing! Keep up the good work! 👍😁
Actually, on a sphere (or any contained surface) you could make a triangle with two obtuse angles. At this point a+b>c no longer necessarily holds.
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 :)
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.
Maybe it's a triangle on a cone. Varying 3D cones have different degrees, like cones that have 10 degrees or 37 degrees even 50 degrees. So the isosceles triangle is on a cone, where the remaining side cuts through the cone exactly and the first two same sides indicate the degrees of the cone. So maybe it's an "isosceles cone", and the formula is actually a way to measure the circumference of the bottom of the cone. It looks triangular from a certain angle, until you realize that it's 3D! So it's possible that it's the formula to calculate the circumference of the bottom of the cone. From there, maybe the cone height and even the cone volume can be calculated. And it we know the weight of the cone, we can use the formula "D=m/v" to calculate the cone density and then put it through the density experiment to see if it floats on oil or sinks in honey or floats on water or maybe floating in alcohol or lamp oil or sinking in galinstan liquid metal alloy. Or maybe it's a pac man cone. An incomplete cone with two sides that meet up in the bottom forming a pac man shape at the bottom of the pac man cone.
It is possible on a sphere if the longest side almost stretches around the whole sphere and the rest is normal. It will make every side connected to each other, so I think it still counts as a triangle.
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.
If I had learned math this way in school, I think I would less suck at it today. Still I am learning things here.
Well done finding the Scarecrow origin of this!
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
"Homer knows isosceles triangles? It's ridiculous." Hahaha. :)
The Pythagorean Theorem but it's the opposite day
a+b
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
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.
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 ...
Maybe intended, maybe sheer luck, but the first frozen scene: 1 mirror + 2 sinks = 3 stalls (left) + 5 stalls (right) = 8 tiles in lenght
In my language, isosceles triage is called as "equal feet triage" and right angle triage is called as "bracket triage". Maybe that's why we not confuse with both.
in the wizard of oz part, he really got a brain, the brain let him think logically, regardless of his answer being correct or not.
Hm, that statement doesn't make too much sense. I mean aren't you contradicting yourself? Logic would imply correctness, no?if he's not correct then that's Logic not working?
Logic does not imply correctness.
Im Dixie
Stating random incorrect facts from nowhere is the opposite of logic, no?
No, that is not the opposite of logic. hth
he did not seem to think in the slightest. he was smarter than any animal before (he could speak!), and the wizard changed nothing.
3:05 He got a brain just not a very good one.
At around 7 minutes, trying to make the Mutilated Pythagorean Theorem (MPT) work on a spherical triangle - the triangle you show won't satisfy it, but there are spherical triangles that do. If you put the apex at a pole, and _c_ along the equator, then _a_ and _b_ are ¼-great-circle arcs ( _a_ = _b_ = ½πR), and _c_ can be any length in the open interval, 0 < _c_ < 2πR.
E.g., if R = 2/π, then _a_ = _b_ = 1, 0 < _c_ < 4. If you could make _c_ the entire equator, you'd have _(a,b,c)_ = (1,1,4), which satisfies the MPT; that is, for sides taken in the order _a,b,c_ ; √a + √b = √c.
If you make _a_ = _b_ a little shorter than 1 and at slightly different "longitudes", then they can be adjusted so that the great circle joining them the long way, will be _c_ = _4a_ = _4b_ , and the MPT will hold.
[Interesting to note: the MPT is homogeneous of degree ½, so it scales by any constant factor without changing.]
Very impressive you could sync up your gestures to the on screen animations so perfectly. Timing and position were on point! How did you do that editing magic?
Maybe he has a projector displaying the slides
2:59 Is it normal that i see some similarities with the mathloger ?
He got the brain, went to Australia and became matematician.
His laugh is adorable. Love it!))
One instance on a sphere where this might work is a sphere so small that the end points of the c side are closer together on the back side of the sphere than when you follow the line between them
The only time this equation works is if all the terms are zero. So he has a point.
It is quite wrong ... but ... it can get even wronger 🤣🤣🤣
When your literature teacher interprets a passage in a book
The video no one really ever needed but it's always good to educate the masses.
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.
That's such a math teacher reaction to a bit such as 'crystal math'.
watch my maths videos to learn something.
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 :)
It can be done on the surface of a cone where the largest side of a triangle is towards the base of the cone compared to the other sides. Also after boiling down variables, I came to a = b + sqrt(2ab) to satisfy sqrt(c)=sqrt(a)+sqrt(b) where a is not equal to b and all three are real non zero numbers. It was a few napkins long of some algebra but it's possible there is a small mistake in there.
Completely unrelated, but it makes you appreciate the prosthetic work on scarecrow way back when.
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.
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.
this man's laugh is so pure
Wow this really takes me back to my High School days. Haven't used formulars and done advanced mathematics since then. Being a social scientist, it's fun to dive into that way of thinking though, it's so different and straightforward.
You still have to use math as a social science, but it's all statistics and basic algebra for graphs.
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
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
I haven't checked this but it seems to me that if c extends almost completely around the sphere at the equator then a+b can equal approximately c/2 if they meet at a pole, which leaves room for a situation where the conditions are met. I guess that stretches the definition of a triangle a bit far given that the internal angles tends towards 3pi. I must confess I have little knowledge of what I'm talking about
Take that same triangle on a sphere then rotate it up while looking straight at it till half the triangle is out of sight. The apparent lengths of the sides from your perspective now satisfy the equation.
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
Wow, never knew that was a Wizard of Oz reference lol
The first clip at the end had a pun with the words sign/sine. The sine of a right triangle relates to the height of a right triangle in relation to the hypotenuse and the sine value is usually smaller than the actual height of the actual triangle.
Bart's "vitamins" include 'Crystal Math' and 'Brozac'