See I wish more teachers while I was still in school explained the reason why math is so important. The only answer I got when I asked "where would I need this" or "why is this important" was "because its on the test" or "its school mandated" rather than explaing that math is integral to the way the world works and functions. This is way more interesting than I remember it being
This video did not explain how the world works. It was a couple historical examples followed by a few different proofs. If you just want to complain about school, go ahead, but don't disguise it as "this 5 minute video taught me a lot about life."
@@SomeRandomDude821 you know people are not needed to be taught they just need a direction to flow in they just need inspiration a way that in which they can relate it You will not remember everything thaught in school your whole life maby if you go to acadamiea you will only know stuff of your field even then that not to detail We nead to teach how to think not what to think Offcourse 5 min is nothing in learning compared to 25 years of school it can never be but the point is how much of it resonates with you
When I asked this: they said it was important so you don’t get scammed when asking for your change. 8th grade… Since then I have figured it out myself and I have actually studied maths myself. I have been teaching myself computer science and have realized the importants of maths even more
1:50 love the attention to detail. “On a flat surface” cause we now know we can make non-Euclidean geometry which breaks these rules by using things like spheres to make a triangle with 3 right angles Edit: fixed error pointed out by Hritik
I kind of stumbled upon that first one in high school, but without the second diagram. I knew (a+b)^2 =a^2+2ab+b^2, and wanted to visualize what that meant geometrically by creating a square with a+b on all sides, using triangles of surface ab/2. 4 Triangles of ab/2 made 2ab, so the remainder of the square that wasn't the triangles had to be a^2+b^2. Unfortunately I never made the leap that this was also c^2 (because I hadn't even considered that side of the triangles), and therefore a proof of Pythagoras, even though it was right in front of me. Just goes to show you sometimes can only find what you are looking for.
Look at this video This is the best demonstration that i have seen mathematically. Actually i believe pythagoras did this way more than 2000 years ago. ruclips.net/video/AnQX3zKq0TU/видео.html
It is also valid for other figures scaled to the sides of the triangle. For example, a circle with diameter equal to the hypotenuse will have an area equal to the sum of the areas of circles formed when the other 2 sides are taken as diameters. Also valid when considering semicircles drawn in the same manner, parallelograms and more.
I use a variation of the 4 triangles, set them up like at 2:24, and find the area of the squares. It is a^2+b^2+2ab for the large square, while the contents of that square are c^2+4(ab/2), subtract 2ab from both areas and you get a^2+b^2=c^2
Incrivel como tudo na matemática tem uma base lógica. Ela se torna cad vez mais linda pra mim. Espero q um dia o Brasil seja um país conhecido pela valorização da matemática.
I saw the water-filled squares proof at the Ontario Science Center in the 1980s and remember thinking to myself, so that's what the square on the hypotenuse means. It was a really meaningful representation.
So extremely helpful!! I'm in a graduate level History of Mathematics class, and this video really helped me to understand the Pythagorean Theorem in a different way.
I have never commented on a TED-ED video. But I have watched nearly all of them, and this is my comment if I had one for every video put together: Wow! Amazing! Keep up the good work! Love the cool art style for this video! I like how you touched on that point! Omg I just learned about that in school! The animations are great! I tried to solve the problem from many differed perspectives, but I didn't know it was that simple! I wish that I could remember all that!... My main point is that over the really REALLY long time that I have been watching TED-ED. To all the animators, and all the educators and all the writers and all the people that helped contribute to the amazing videos that you guys upload, Thank You! Over the years I have learned a lot from this channel. And maybe one day, I'll be in one of my own TED-ED video!
I got a riddle for you: What is the creature that walks on four legs in the morning, two legs at noon and three in the evening? If you guess it correct you will be king of Thebes and marry your mother.
wish schools would teach us things like this, it makes learning about math so much more interesting because you can see its real life applications and its actually really fascinating, i think more people would enjoy and excel at math if we were first shows things like this before being taught concepts
I think TedED deserves support, they're giving easy to understand education videos that aren't sponsored and don't have ads.... And asking you politely to consider isn't like forcing you with "This video is sponsored by Raid Shadow Legends" while watching.
the proof @ 1:30 is often used in art, such as figure drawing in this example, when combining parts of the body so that they stay within the correct proportions.
Another proof by rearrangement that ends in an algebraic solution: Get 4 exact triangle copies and connect them as in the first step of example one in the video where a square of c^2 is in the center. If we look at the outer square that this forms, the side lengths are (a+b) so it’s area is (a+b)^2. Now we need to find the area of all 4 triangles combined 2 different ways and then set them equal and solve. 1- take the area of a single triangle 1/2 base* height and multiply that by 4. We end up with 2ab. 2-subtract the inner square from the outer square. This gives us (a+b)^2 - c^2. Set method 1 and 2 equal to each other. This gives: 2ab = (a+b)^2 - c^2 This simplifies to a^2+b^2=c^2. QED
In case anyone is using this to learn more math, 1:48 is not quite right. 2a^2=c^2 would imply a/c=sqrt(2), which would make sqrt(2) rational. The graphics makes it look like two of the a^2 squares would fit inside the bigger c^2 square (that triangle looks like it’s a perfect fourth of the square), but the a^2 squares are always just a tad off ... exactly one unit area off actually. You can see for example 2*2^2=8=3^2-1, or 2*5^2=50=7^2+1.
The geometric demonstrations of it are always neat, but my favourite proof is the one that emerges naturally from complex numbers. It then comes right out of the fundamental arithmetic of multidimensional numbers, all on its own.
It doesn’t necessarily mean that. The area of a rectangle is Its length L times its width W; a square is just a rectangle with equal sides so, L=W, therefore A=L•L or L^2.
Ηere's my proof (I'm sure it has been found by others many times before, altough I am not sure by whom exactly). I found it accidentally: For any right triangle, the trigonometric identity (sinθ)^2 + (cosθ)^2 = 1 holds true for any angle. Let "a" and "b" be the adjacent sides and "c" the hypotenus. By expanding the definition of the trigonometric numbers in the identity we get: (a/c)^2 + (b/c)^2 = 1 (a^2/c^2) + (b^2/c^2) = 1 Multiplying by c^2: a^2 + b^2 = c^2 Q.E.D. It's definetly not much. But I was super proud when I came across it.
Adrian Spencer Elizalde I was the exact opposite. I absolutely loved geometry and logical proofs, but struggled terribly with algebra and calculus. Then again I was skipped ahead a year in middle school, so technically I actually never took Algebra 1 (I never even learned how to factor!) And that screwed up my entire math career. Still, such divisions make me wonder about how differences is personality, thinking patterns, brain structure, etc. may account for different math preferences. Personally, I have always considered myself a "visual learner." I can't play any instruments where I can't look down at what I'm doing, so I excelled only in drums and piano. And even when I play the piano, I can't read sheet music. I memorize the keys and which order to press them in by creating a series of shapes in my mind (e.g. I always think of Für Elise as the "three isosceles triangles song"). Being so visual made Geometry come naturally to me. I wonder what types of minds are drawn towards Algebra, Statistics, and Calculus?
Here’s my proof: Take the square from 2:29 The length of the large square is (a+b) squared because the length of one side of the large square is the length of a plus the length of b, making a square that has a+b as a side length The area of c^2 is the area of the large square minus the triangles The area of a triangle is ab/2 (because one triangle is a rectangle with side lengths a and b which is cut diagonally) and since there are four triangles, the total area of the triangles is 2ab The total area is (a+b) squared, which is a^2+2ab+b^2 and you subtract the 2ab from the four triangles, you get a^2+b^2= the area of the square of c, or a^2+b^2=c^2
Even though the Pythagorean Theorem was know before Pythagoras, it was Pythagoras who first gave a rigorous proof, and the concept of a mathematical proof originates from the Greeks. Hence we named it after him. As for the water turntable demonstration towards the end of the video, it is not admissible as a mathematical proof. Lengths are specific rather than general.
I have a simple way to prove the Pythagorean theorem, you have 3 squares, the 1st square has an area of 4cm², the 2nd square has an area of 8cm², the final square has an area of 12cm². If you combine the 1st and 2nd squares, you get an octagon with an area of 12cm² (4cm² plus 8cm2) which is equal to the area of the third square (12cm²)
@AMAM JAIN I am not sure how you took my comment but I was just being informative about who they were and where they stood inside the culture. I don't mind him saying he looks cute at all🤣🤣🤣
Also note that if c is given, you can graph y = ±√(c^2 - x^2) to get a circle. Now you're actually ready to start trigonometry, instead of just pressing sin and cos on a calculator to get an answer.
My favorite: Triangle is 3 vectors, a, b and c with c = a + b. Now square that (dot product), get c^2 = a^2 + b^2 + 2a.b cos(x) where x is the angle of a and b. For a right triangle cos (x) is zero.
method at 3:41 can also be done by just saying that the area of each triangle is proportional to the square of the hypotenuse. since sum of areas of two smaller triangles is equal to the area of the larger triangle. then the sum of the squares of the hypotenuses of the two smaller triangles(a² +b²) is equal to the square of the hypotenuse of the larger triangle ( c²)
And now ,in 2023,there is an ingenious trigonometric proof which does not circularly rely on the Pythagorean identity iself in the first place, conceived by 2 high school students.
2:24 We don't even need to do the second step at 2:30. We can simply obtain 2 different equations to calculate the area of the big square. The area of a square is equal to its side squared. The side of the big square is a+b so: A = (a + b)^2 = a^2 + b^2 + 2ab But we can also calculate the area as the sum of the areas of all 4 right angle triangles and the square in the middle. The area of a right triangle is a*b/2. Therefore: A= (4*a*b/2) + c^2 = 2ab + c^2 We can now set these two different formulas for the area equal: a^2 + b^2 + 2ab = c^2 + 2ab Subtract 2ab on both sides and we get: a^2 + b^2 = c^2
Here is my proof: The triangle has 3 edges Edges has 5 letters 5-3=1431879-1431877=2 Number 1431879 for what? Of course That's Einstein's birthday: 14/3/1879 14/3-->3/14 3/14-->3.14 What does the number 3.14 relate to? Yes Of course Anyone who is good at Math will know That's 3x14=42 42 is *THE ANSWER TO LIFE THE UNIVERSE AND EVERYTHING*
My solution was to make the formation at 2:25 and then subtract the four triangles from the whole figure. (a+b)^2 - 4(0.5ab)=c^2 (a^2 + 2ab + b^2) - 2ab = c^2 a^2 + b^2 = c^2 Another proof that I made was to use the formula that finds the length between two points on a graph and center the vertex of the triangle at the origin and the sides a and b on the x and y axis sqrt( (a-0)^2 - (0-b)^2) = c (a-0)^2 - (0-b)^2 = c^2 a^2 - b^2 = c^2
@@andrewwwjo Ok I get that this is probably a joke but just to specify for anyone who didn't see where I got the a+b in solution one, if you look at one of the sides on the whole figure at 2:25, the side lengths are the a and b sides of your right triangle. Because the figure is a square, to find the area you have to square the side lengsths, resulting in (a+b)^2.
but if the angle is not 90 degrees, c^2 = a^2 + b^2 - 2ab*cos(gamma) whereas gamma is the corner which should be 90 degrees, but is not. cos(90) = 0, so a lot of people forget about the second part of the theorum.
Different theory. In school we called it the law of cosine whereas the law of sin is (A/sin a) = (B/sin b) = (C/sin c) where A, B and C are the the sides facing the angles a, b and c in that order. But both of these are more like expansions to the one in the video.
That's a different theorem. Pythagoras is for triangles which have an angle of 90°. If you're given a non-rectangle triangle, then you should apply Sine and Cosine theorems.
We learnt the Pythagoras theorem in 5th grade. Did you know that there is an alternate, simple and ancient Indian method to compute hypotenuse : The Tamil kings, centuries before the dawn of the Common Era had built dams, dykes, palaces and great cities during the Sangam era. How did the architects in those times design and build the great turrets in temples and the great dams,canals, highways, etc. Upon searching it was revealed that finding the hypotenuse of a right-angle triangle can be done independent of the Pythagoras theorem, (which enunciates that sum of the square of both sides of the right angle will be equal to the square of the hypotenuse, of the triangle). It is a simple task to find the square of a number, but finding the square root of a number is not so easy. There is no simple formula to find the square root of a number. An ancient Tamil mathematician/poet Pothayanar, who lived 800 years before the Common Era, had given a quatrain of four lines articulating the method of finding the length of the hypotenuse of a right-angle triangle without the need to find the square or the square-root, only using the length of the sides, and simple fractions. Here is the English translation of the quatrain: Divide the horizontal into eight, Delete one portion, and add the remaining, to half of vertical to result you’ve got. The answer would be hypotenuse of the triangle. The Tamil poem by poet Pothayanar is : ஓடும் நீளம் தனை ஒரேஎட்டுக் கூறு ஆக்கி கூறிலே ஒன்றைத் தள்ளி குன்றத்தில் பாதியாய்ச் சேர்த்தால் வருவது கர்ணம் தானே. - போதையனார் The advantage of the ancient theorem is that there is no need to use a square / square root function. But before we jump to conclusions let us see how this ancient and simple formula works : Let us take the three sides of the right-angle triangle to be A, B, and C, where C be the hypotenuse. Let us take A and B to be the horizontal and perpendicular sides respectively. If we are to divide A into eight parts and takeaway one eight, it would be 7/8A. The half of the vertical side will be 1/2B. Thus, the result should be : C= 7/8A + 1/2B Let us give some numbers and try : *Firstly* Say A=8 and B=6 By Pythagoras theorem, C equals √ (8x8+6x6) Which is √ (64+ 36) = √100 =10. Now, according to the quatrain : C should be 7/8 A+ ½ B 7/8 of A (8) = 7 and ½ of B (6) =3 Together they add up to give hypotenuse to be 7+3=10
*Second* let us try with taking A=28 and B=21 then by Pythagoras theorem C= √ (21x21+28x28) C = √ (441+784) which is =√1225 = 35 According to quatrain : hypotenuse becomes 7/8A + 1/2 B. 7/8 A=7/8 (28) = 24.5 and 1/2B= 1/2 (21) = 10.5 Thus 24.5 + 10.5= 35. *Third* let us try with taking A= 12 and B= 5 then By Pythagoras theorem C= √ (12x12) + (5x5) = (144+ 25) √169 =13. According to the ancient Tamil quatrain : the hypotenuse becomes 7/8A + 1/2B 7/8(12) = 10.5 1/2 (5) = 2.5 Thus 10.5 +2.5 =13 Pothayanar must have been a great mathematician, who got lost like fruit hidden in the foliage of the tree. The discoveries of the Greek scientists and mathematicians spread far and wide along with their conquests in the world. Unfortunately, in ancient India, many great intellectuals, and their knowledge / findings were lost to the world owing to various reasons and events. Our schools teach the Pythagoras Theorem to our children. They should also teach Pothayanar's theorem as an alternate and easier method, as explained above.
Doesn’t work with 7,24,25. Or with any right triangle with irrational sides. It only works for triangles with ratios 3:4:5 and 5:12:13 which is probably why its not commonly used.
I remember when I learned this me and my dad had built a shed with a slanted roof and we didn't know how long the top had to be. the next day I walked into my geometry class and told my teacher I had used the Pythagorean theorem on my shed. she was super excited until I said "just kidding I used a tape measure like a normal person." WORTH IT
I think that the fact that the 4 identical right triangles can be arranged into one square in such a way that their hypotenuses make a tilted square is an observation in itself; can't see how that can be taken for granted.
@Clint Eastwood pls once see ancient books on hindus , everything in maths science etc etc is written there also i am non-hindu but now i am adopting hinduism
Math is really fun. A single theorem can have multiple proofs - as in programming, a problem can have multiple solutions. I remember back in school when we started learning the Pythagorean theorem. The way my teacher used to explain was too boring that if she had explained in such a way that we will use it in our real lives, with showing examples, it would be much more interesting and more students would remember the given information. In fact, one of the best ways to explain mathematics is to visualize them if possible. For me, when I do not understand a proof, or a solution, the best way I will understand it is through graphs which would be kept in my memory for later.
Using Alkashy theorem in right angled triangle 90 having two adjascent sides a and b and the opposite side as c ,c^2 = a^2+ b^2 - 2 a b cos theta as cos 90 is zero and hence a^2+ b^2 = c^2 proving pythsorean theorem.
![Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]](http://i.ytimg.com/vi/p6j2nZKwf20/mqdefault.jpg)
See I wish more teachers while I was still in school explained the reason why math is so important. The only answer I got when I asked "where would I need this" or "why is this important" was "because its on the test" or "its school mandated" rather than explaing that math is integral to the way the world works and functions. This is way more interesting than I remember it being
And it helps remembering things!
This video did not explain how the world works. It was a couple historical examples followed by a few different proofs. If you just want to complain about school, go ahead, but don't disguise it as "this 5 minute video taught me a lot about life."
@@SomeRandomDude821 you know people are not needed to be taught they just need a direction to flow in they just need inspiration a way that in which they can relate it
You will not remember everything thaught in school your whole life maby if you go to acadamiea you will only know stuff of your field even then that not to detail
We nead to teach how to think not what to think
Offcourse 5 min is nothing in learning compared to 25 years of school it can never be but the point is how much of it resonates with you
This
When I asked this: they said it was important so you don’t get scammed when asking for your change.
8th grade…
Since then I have figured it out myself and I have actually studied maths myself. I have been teaching myself computer science and have realized the importants of maths even more
Me:Yo pass the _right angled ruler_
Friend:You better not to _prove the Pythagorean Theorem_
Me:
True Pug Lord it's called a set square
True Pug Lord NVM
an example is never a proof.
this is my favorite thing
Lol 666 likes
1:50 love the attention to detail. “On a flat surface” cause we now know we can make non-Euclidean geometry which breaks these rules by using things like spheres to make a triangle with 3 right angles
Edit: fixed error pointed out by Hritik
Woah cool
Yeah thats so right. Cool. -And btw you meant --1:50-
@@hritikvaishnav603 that's what he said..
@@rawanmalatani39 oh they might have fixed it now. Earlier it was wayy off. And I got confused af
@@rawanmalatani39 yeah the commenter edited it
I kind of stumbled upon that first one in high school, but without the second diagram.
I knew (a+b)^2 =a^2+2ab+b^2, and wanted to visualize what that meant geometrically by creating a square with a+b on all sides, using triangles of surface ab/2.
4 Triangles of ab/2 made 2ab, so the remainder of the square that wasn't the triangles had to be a^2+b^2.
Unfortunately I never made the leap that this was also c^2 (because I hadn't even considered that side of the triangles), and therefore a proof of Pythagoras, even though it was right in front of me. Just goes to show you sometimes can only find what you are looking for.
Look at this video This is the best demonstration that i have seen mathematically. Actually i believe pythagoras did this way more than 2000 years ago. ruclips.net/video/AnQX3zKq0TU/видео.html
That’s so interesting!!
IK you can find so much if you just work hard enough
Here's my prove: Ted Ed made a video about it.
Yeah
lol😂
@@aayush_7037 bondade
@@Tenzinforeal Negi
@@aayush_7037 yes😌
Anyone else notice that their eyebrows are made out of right triangles?
Justin Xia 2:09 is that a right triangle?
It is if you are looking at it from a 3 dimensional view point. But that would be another Ted Talk. ;) Anyway, at least Justin didn't say *all*.
K.
Pythagoras’ eyebrows at 4:46 are definitely not right triangles, or maybe they never are
Nerd freak
Here's my proof:
It works
It's only a proof if you tried all possible triangles. Which is impossible to do, as there is an infinite number of possible triangles.
uncountably, in fact
OMG! It does! LOL
The Ace Of Spades Here another proof:
ruclips.net/video/mdU8dyjgXU0/видео.html
The Pythagorean Theorem can be weaponized.
That's not how you prove something in math, but it is how you prove something in science.
What an insightful video! Keep up the amazing work!
lol n00b boi
my like is no 600!!!
It is also valid for other figures scaled to the sides of the triangle. For example, a circle with diameter equal to the hypotenuse will have an area equal to the sum of the areas of circles formed when the other 2 sides are taken as diameters. Also valid when considering semicircles drawn in the same manner, parallelograms and more.
I use a variation of the 4 triangles, set them up like at 2:24, and find the area of the squares. It is a^2+b^2+2ab for the large square, while the contents of that square are c^2+4(ab/2), subtract 2ab from both areas and you get a^2+b^2=c^2
I wish I was high on potenuse.
Ayyy, nice one!
DethroneME dude that was my joke...
Key and peele! loool
*gives you a medal from Obama*
key & peele
The animations of the mathematicians were funny
Ace132 Most of the content TedEd produces falls on deaf ears.
FarCritical lol
Craig Sundaram What? I can't hear you from a top my horse.
Did you mean "the"?
lol
And if my Maths teacher, back in the day, just drew a right angle triangle with 3 squares attached he would have saved both of us a lot of time haha.
Lies again? Plane Ticket USD SGD
The way, through the funny animations the pythogoras theorem was explained is completely praise worthy. Simply awesome 👍👏😊
Incrivel como tudo na matemática tem uma base lógica. Ela se torna cad vez mais linda pra mim. Espero q um dia o Brasil seja um país conhecido pela valorização da matemática.
Step 1: Take a triangular sandwich of your choice that has a right angle.
Step 2: Eat it.
Instructions unclear. Choking on set square.
@@LughSummerson Lol
Why would I eat a witch made of sand? Choke alert! This comment is not safe for children of age 3 years or less
I think Euclid did the naught.
@@kyled1673 lol
are we not going to acknowledge the fact that einstein came up with a proof of the pythagorem theorem at 12????
Yeah, and still some people believe he was bad at maths when he was young. lol
omg he is the genius of all time.
Yalena Gloria he is a genius, but proving Pythagoras isn't exactly difficult. It's one of the most basic theorems in all maths (these days)
Ibno Zizou
Yep
Flying Swordfish yeah but when it was einstein's time it wasn't
Hi (Sorry for my bad english)
wtf Im laughing
Sorry for my bad english (Hi)
Heroo, sawlee foooor mie baaddd engrsh
Bukan Hamid Grammar pls. cx
Hai (Sila maafkan penguasaan Bahasa Malay saya yang lemah)
Glad to see someone young was able to prove this theorem
they are ancient Egyptian. They look Afro-Asiatic Proof once more again = THE TRUTH IS STUBBORN
@@cinnamonstar808 ???
@@cinnamonstar808that makes no sense
I saw the water-filled squares proof at the Ontario Science Center in the 1980s and remember thinking to myself, so that's what the square on the hypotenuse means. It was a really meaningful representation.
So extremely helpful!! I'm in a graduate level History of Mathematics class, and this video really helped me to understand the Pythagorean Theorem in a different way.
I have never commented on a TED-ED video. But I have watched nearly all of them, and this is my comment if I had one for every video put together:
Wow! Amazing! Keep up the good work! Love the cool art style for this video! I like how you touched on that point! Omg I just learned about that in school! The animations are great! I tried to solve the problem from many differed perspectives, but I didn't know it was that simple! I wish that I could remember all that!...
My main point is that over the really REALLY long time that I have been watching TED-ED. To all the animators, and all the educators and all the writers and all the people that helped contribute to the amazing videos that you guys upload, Thank You! Over the years I have learned a lot from this channel. And maybe one day, I'll be in one of my own TED-ED video!
The way that Euclid touches young Einstein at 3:05 makes me feel uncomfortable
Einsteins expression is the thing that makes it weird.
Why does he stick his tongue out tho like wtf
Lol, the way you stared at me at 9.23 according to my clock made me feel even more uncomfortable 🤭😁
Oh
Yeah I realised that but it’s just fucken weird how he sticks his tongue out as soon as a man touches his shoulder.
Einstein came up with a proof of the Pythagorean theorem at 12
Asian baby: hold my pacifier....
Er, that’s kind of a myth
@@piyushxcoder who's that person?
Yeah meanwhile me an Asian kid searching for solution for every dam question
@@farismustafa5389 HE WAS AN INDIAN PHILOSOPHER/MATHEMATICIAN/PHYSICIST BORN IN BETWEEN 4TH AND 6TH CENTURY BCE(UNCLEAR BIRTH DATE).
@@piyushxcoder That guy had work that is completely different from Einstein’s.
That background music at 4:56 was awesome. As I had dolby speakers I felt as if it was coming from somewhere else other than my speaker!
4:28 Like anyone got time for that
Clovey I know right😂😂
Clovey, DIYers have the time for anything
It helped me in my math project xd
have time for Fortnite, have time for that
people with no life: *allow me to introduce myself.*
Please upload A Riddle
The Channel yea
The Channel i dont mind ads
i dont mind buffer
But When Ads Buffer
I Suffer
And Also : Wtch - Will Magnets Work In Outer Space? In My Chan
MyThoughts yep earth is a giant magnet mate
The Channel I support you for this
I got a riddle for you: What is the creature that walks on four legs in the morning, two legs at noon and three in the evening?
If you guess it correct you will be king of Thebes and marry your mother.
I think that many cultures figured this out is amazing, and that our universe just had this mathematical phenomenon
Yes in India, hundreds of years before Pythagoras, Baudhayan speculated the exact theorem for rectangles.
wish schools would teach us things like this, it makes learning about math so much more interesting because you can see its real life applications and its actually really fascinating, i think more people would enjoy and excel at math if we were first shows things like this before being taught concepts
Me: 4:56
"Did you enjoy this lession?
If so consider please consider supp-"
**video closed**
Well clearly not cuz you had time to comment this but ye I normally do that with videos like these
I think TedED deserves support, they're giving easy to understand education videos that aren't sponsored and don't have ads....
And asking you politely to consider isn't like forcing you with "This video is sponsored by Raid Shadow Legends" while watching.
@@monochromeart7311 they have ads ._.
@@blindvi4849 ads aren't much of an income for many people....
@KARL KFOURY not to mention, they would need atleast 3 videos a month for minimum wage (in America) for a single person (if it's indeed 2K per video)
please do a video about thales
Yes please
thank you ted-ed for continuing to enlighten me on topics i was always curious about, but never really finding out.
the proof @ 1:30 is often used in art, such as figure drawing in this example, when combining parts of the body so that they stay within the correct proportions.
Another proof by rearrangement that ends in an algebraic solution:
Get 4 exact triangle copies and connect them as in the first step of example one in the video where a square of c^2 is in the center. If we look at the outer square that this forms, the side lengths are (a+b) so it’s area is (a+b)^2.
Now we need to find the area of all 4 triangles combined 2 different ways and then set them equal and solve.
1- take the area of a single triangle 1/2 base* height and multiply that by 4. We end up with 2ab.
2-subtract the inner square from the outer square. This gives us (a+b)^2 - c^2.
Set method 1 and 2 equal to each other.
This gives:
2ab = (a+b)^2 - c^2
This simplifies to a^2+b^2=c^2.
QED
@Carson Middleton thanks!
In case anyone is using this to learn more math, 1:48 is not quite right. 2a^2=c^2 would imply a/c=sqrt(2), which would make sqrt(2) rational. The graphics makes it look like two of the a^2 squares would fit inside the bigger c^2 square (that triangle looks like it’s a perfect fourth of the square), but the a^2 squares are always just a tad off ... exactly one unit area off actually. You can see for example 2*2^2=8=3^2-1, or 2*5^2=50=7^2+1.
a/c is always irrational check for yourself my dear sir
I just want to impress random strangers on the Internet.
TMR Teckk Impressed random stranger on the internet passing by.....
wow. Im so impressed.
Impressive.
Tehcookie vanilla Heyy fellow rocket league player... Dota player repprting in.
V.I.P Slayer PogChamp!!
The geometric demonstrations of it are always neat, but my favourite proof is the one that emerges naturally from complex numbers. It then comes right out of the fundamental arithmetic of multidimensional numbers, all on its own.
I LITERALLY NEVER KNEW "squared" ACTUALLY MEANT A SQUARE LIKE THAT OMG
*everything makes sense now*
When we just memorize plug-and-chug calculations or use calculators, we'll never understand math at all.
@Zubeen Bhuiyan It is. You shouldn't just rote stuff without knowing what they actually mean in the real world.
It doesn’t necessarily mean that. The area of a rectangle is Its length L times its width W; a square is just a rectangle with equal sides so, L=W, therefore A=L•L or L^2.
If you have a line of length a, then a^3 would be the volume of a cube with side length a! Tadah
Ηere's my proof (I'm sure it has been found by others many times before, altough I am not sure by whom exactly). I found it accidentally:
For any right triangle, the trigonometric identity (sinθ)^2 + (cosθ)^2 = 1 holds true for any angle.
Let "a" and "b" be the adjacent sides and "c" the hypotenus. By expanding the definition of the trigonometric numbers in the identity we get:
(a/c)^2 + (b/c)^2 = 1
(a^2/c^2) + (b^2/c^2) = 1
Multiplying by c^2:
a^2 + b^2 = c^2 Q.E.D.
It's definetly not much. But I was super proud when I came across it.
It's not a proof because the conclusion is self contained within your original assumption.
Indian mathematician name was boudhayana, who described it in his writings shulbha sutras(easy formulas).
I love ted end it makes me feel relaxed when learning new things
even though I hate maths
You probably don't actually hate math. My guess is you just hate the lazy way it is often presented in schools.
This was super informative and I'm glad it showed multiple proofs
305 proofs. I guess it must be true then... :)
afhdfh Well ,it was "true" to begin with. This just gave more evidence to prove it is more "true".
It's true with just one proof.
Yes. But this makes it ultra true! ;)
It said more than 350 proofs
So...?
Take a triangle of sides a,b,c and angles A B C and b is right angled
Now A+C=90
now sin(A+C)=1
SO NOW
SinAcosC+Cosasinc=1
b2+a2=c2
The trig identities are derived from the Pythagorean theorem...
@@santiago_moralesduarte yes
Thanks for this TED-Ed and Betty Fei!
Ted- How many ways to prove Pythagoras theorem
Me - By using perpendicular triangle.
lol,Is that even a thing? Maybe a product of your imagination. Cool!
Perpendicular triangle, parallel points, congruent points, 2 non-coliniar points, obtuse point...
Geometry was never really my thing back in high school. I did poorly in proving. Algebra, Statistics, and Calculus are my favourites.
hears calculus
*screams in terror*
PROOFS ARE THE WORST!
I was pretty ok in geometry, but whenever I hear the word proof I want to tear something up. (I'm also an algebra person.)
Yalena Gloria That's how Japanese students react after scary tales of this: ruclips.net/video/mdU8dyjgXU0/видео.html
Adrian Spencer Elizalde I was the exact opposite. I absolutely loved geometry and logical proofs, but struggled terribly with algebra and calculus. Then again I was skipped ahead a year in middle school, so technically I actually never took Algebra 1 (I never even learned how to factor!) And that screwed up my entire math career. Still, such divisions make me wonder about how differences is personality, thinking patterns, brain structure, etc. may account for different math preferences. Personally, I have always considered myself a "visual learner." I can't play any instruments where I can't look down at what I'm doing, so I excelled only in drums and piano. And even when I play the piano, I can't read sheet music. I memorize the keys and which order to press them in by creating a series of shapes in my mind (e.g. I always think of Für Elise as the "three isosceles triangles song"). Being so visual made Geometry come naturally to me. I wonder what types of minds are drawn towards Algebra, Statistics, and Calculus?
Trigenometry and calculus were my faves.
TED-ED a day keeps bad grades away.
I added one method using circles and for your kind information I did it in summer vacation when I was in class 8
I don't know how to send link of my method otherwise I would have posted it
Here’s my proof:
Take the square from 2:29
The length of the large square is (a+b) squared because the length of one side of the large square is the length of a plus the length of b, making a square that has a+b as a side length
The area of c^2 is the area of the large square minus the triangles
The area of a triangle is ab/2 (because one triangle is a rectangle with side lengths a and b which is cut diagonally) and since there are four triangles, the total area of the triangles is 2ab
The total area is (a+b) squared, which is a^2+2ab+b^2 and you subtract the 2ab from the four triangles, you get a^2+b^2= the area of the square of c, or a^2+b^2=c^2
Even though the Pythagorean Theorem was know before Pythagoras, it was Pythagoras who first gave a rigorous proof, and the concept of a mathematical proof originates from the Greeks. Hence we named it after him. As for the water turntable demonstration towards the end of the video, it is not admissible as a mathematical proof. Lengths are specific rather than general.
Love these videos
Naja I
Hmm. This makes me wonder. Did all cultures around the world discover the theorem independently?
I doubt such deliberately un-mathematical societies as the Romans produced any original proofs.
@@jessehammer123 The Romans used math heavily lol. They were master architects.
Africans certainly didn't discover anything useful. Ever
@@yvesnyfelerph.d.8297 en.wikipedia.org/wiki/History_of_science_and_technology_in_Africa
Yes. Many cultures found it independently
Thanks. Explained in 5 minutes what some teachers struggled to explain on the course of multiple classes.
I have a simple way to prove the Pythagorean theorem, you have 3 squares, the 1st square has an area of 4cm², the 2nd square has an area of 8cm², the final square has an area of 12cm². If you combine the 1st and 2nd squares, you get an octagon with an area of 12cm² (4cm² plus 8cm2) which is equal to the area of the third square (12cm²)
I love these videos...makes me feel smart
I hope you do more videos about math , this is interesting.
1:32 this Indian mathematician is one of the cutest thing I've seen on the internet recently 😂♥️
These are known as rishis Or
Brahmans (those who study rhe universe) and had generally the utmost respect in ancient times🥺
Finally I was looking for this comment 🖤🖤
@AMAM JAIN I am not sure how you took my comment but I was just being informative about who they were and where they stood inside the culture. I don't mind him saying he looks cute at all🤣🤣🤣
These are how Indian priests used to dress
@@PranabMallick. 😂😂
I wish I saw this earlier when i was getting introduced to Pythagoras theorem and I hated it. This makes things so much intresting
Also note that if c is given, you can graph y = ±√(c^2 - x^2) to get a circle. Now you're actually ready to start trigonometry, instead of just pressing sin and cos on a calculator to get an answer.
Who is here after the two teenagers found another way to prove the Pythagorean theoreom using trigonometry?
1:37 that theorem is called "Baudhayana Sulbasutra"
My favorite: Triangle is 3 vectors, a, b and c with c = a + b.
Now square that (dot product), get c^2 = a^2 + b^2 + 2a.b cos(x) where x is the angle of a and b. For a right triangle cos (x) is zero.
method at 3:41 can also be done by just saying that the area of each triangle is proportional to the square of the hypotenuse. since sum of areas of two smaller triangles is equal to the area of the larger triangle.
then the sum of the squares of the hypotenuses of the two smaller triangles(a² +b²) is equal to the square of the hypotenuse of the larger triangle ( c²)
Need to update the video now that there is a new method using Trig :)
When you have to learn pythagoras and trigonometry in yr 7
Im on year 8 and we have this as our Special Subject
Very happy to see an intelligent Indian who derived this theorem .
Love from India 🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳
And now ,in 2023,there is an ingenious trigonometric proof which does not circularly rely on the Pythagorean identity iself in the first place, conceived by 2 high school students.
2:24 We don't even need to do the second step at 2:30.
We can simply obtain 2 different equations to calculate the area of the big square. The area of a square is equal to its side squared. The side of the big square is a+b so:
A = (a + b)^2 = a^2 + b^2 + 2ab
But we can also calculate the area as the sum of the areas of all 4 right angle triangles and the square in the middle. The area of a right triangle is a*b/2. Therefore:
A= (4*a*b/2) + c^2 = 2ab + c^2
We can now set these two different formulas for the area equal:
a^2 + b^2 + 2ab = c^2 + 2ab
Subtract 2ab on both sides and we get:
a^2 + b^2 = c^2
Here is my proof:
The triangle has 3 edges
Edges has 5 letters
5-3=1431879-1431877=2
Number 1431879 for what?
Of course
That's Einstein's birthday: 14/3/1879
14/3-->3/14
3/14-->3.14
What does the number 3.14 relate to?
Yes
Of course
Anyone who is good at Math will know
That's 3x14=42
42 is *THE ANSWER TO LIFE THE UNIVERSE AND EVERYTHING*
Wot
Yep thats right (didnt get a thing)
@@georgehajnal2723 Oh, makes sense now
@@georgehajnal2723 I'm sorry but, edible colors?
_What's the difference between Euclid, twelve-year-old Einstein and James Garfield? Answer: Nothing! They all enjoy lasagna! Stop!_
They all have right triangle eyebrows
They didn't have lasagna at the time! They have played fidget spinner instead!
I was genuinely shocked when I heard James Garfield was a mathematician, I mostly knew him as the forgotten president that got shot by a nutjob
Me in year 7: Pythagoras
Me in year 8: Trigonometry
Me in year 9: Could we use Trigonometry to prove Pythagoras?
Yes,we could.
S
Take a triangle and apply identity
Trigonometric identities are on pythagoras theorem
@@maheshtagaram9602 which of the three identities ?
The animation makes it look so easy and this theory I never understood in my entire school life
I was literally thinking about this and now this was in my recommendation
My solution was to make the formation at 2:25 and then subtract the four triangles from the whole figure.
(a+b)^2 - 4(0.5ab)=c^2
(a^2 + 2ab + b^2) - 2ab = c^2
a^2 + b^2 = c^2
Another proof that I made was to use the formula that finds the length between two points on a graph and center the vertex of the triangle at the origin and the sides a and b on the x and y axis
sqrt( (a-0)^2 - (0-b)^2) = c
(a-0)^2 - (0-b)^2 = c^2
a^2 - b^2 = c^2
I dont even understand what ur saying lol a+b stuffs
@@andrewwwjo Ok I get that this is probably a joke but just to specify for anyone who didn't see where I got the a+b in solution one, if you look at one of the sides on the whole figure at 2:25, the side lengths are the a and b sides of your right triangle. Because the figure is a square, to find the area you have to square the side lengsths, resulting in (a+b)^2.
Who's here after teens found a trigometry proof for Pythagorean theorem
Yes, i was looking for some known proves.
👋
🙋♂️
✌️
Me: Triangle could never be square.
Triangle: **is square**
Lol 🙃
Well if you turn atto the right posture then you can see it
Very interesting video! The water demonstration is an easy one to remember! 👍
This video teach me all about Pythagoras theorem. Thanks 😉
I love Ted ed
I just got so much hype bc of watching this. Felt like my IQ has increased
✨the next einstein✨
@@georgehajnal2723 shut it geroge
Man, i'm just happy it works, I don't care how many ways there are to prove it.
Thank you so much for uploading this video. It is helping me get through the pandemic!
Wowzers! Thanks for this information! I’m going to tell my hubby about it LOL
but if the angle is not 90 degrees,
c^2 = a^2 + b^2 - 2ab*cos(gamma)
whereas gamma is the corner which should be 90 degrees, but is not.
cos(90) = 0, so a lot of people forget about the second part of the theorum.
Wat?
You are talking about two different theorems...
Pls speak English
Different theory. In school we called it the law of cosine whereas the law of sin is (A/sin a) = (B/sin b) = (C/sin c) where A, B and C are the the sides facing the angles a, b and c in that order.
But both of these are more like expansions to the one in the video.
That's a different theorem. Pythagoras is for triangles which have an angle of 90°. If you're given a non-rectangle triangle, then you should apply Sine and Cosine theorems.
351. Recently a new proof was observed
BRING THE RIDDLE VIDEO BACK ATLEAST 1 IN A WEEK
ahem *once a week
Two 18 years in the US figured this out recently. Great achievement!
Best Pythagorean video
We learnt the Pythagoras theorem in 5th grade.
Did you know that there is an alternate, simple and ancient Indian method to compute hypotenuse :
The Tamil kings, centuries before the dawn of the Common Era had built dams, dykes, palaces and great cities during the Sangam era. How did the architects in those times design and build the great turrets in temples and the great dams,canals, highways, etc.
Upon searching it was revealed that finding the hypotenuse of a right-angle triangle can be done independent of the Pythagoras theorem, (which enunciates that sum of the square of both sides of the right angle will be equal to the square of the hypotenuse, of the triangle).
It is a simple task to find the square of a number, but finding the square root of a number is not so easy. There is no simple formula to find the square root of a number.
An ancient Tamil mathematician/poet Pothayanar, who lived 800 years before the Common Era, had given a quatrain of four lines articulating the method of finding the length of the hypotenuse of a right-angle triangle without the need to find the square or the square-root, only using the length of the sides, and simple fractions.
Here is the English translation of the quatrain:
Divide the horizontal into eight,
Delete one portion, and add the remaining,
to half of vertical to result you’ve got.
The answer would be hypotenuse of the triangle.
The Tamil poem by poet Pothayanar is :
ஓடும் நீளம் தனை ஒரேஎட்டுக்
கூறு ஆக்கி கூறிலே ஒன்றைத்
தள்ளி குன்றத்தில் பாதியாய்ச் சேர்த்தால்
வருவது கர்ணம் தானே. - போதையனார்
The advantage of the ancient theorem is that there is no need to use a square / square root function.
But before we jump to conclusions let us see how this ancient and simple formula works :
Let us take the three sides of the right-angle triangle to be A, B, and C, where C be the hypotenuse.
Let us take A and B to be the horizontal and perpendicular
sides respectively.
If we are to divide A into eight parts and takeaway one eight, it would be 7/8A.
The half of the vertical side will be 1/2B.
Thus, the result should be :
C= 7/8A + 1/2B
Let us give some numbers and try :
*Firstly* Say A=8 and B=6
By Pythagoras theorem, C equals √ (8x8+6x6) Which is √ (64+ 36) = √100 =10.
Now, according to the quatrain :
C should be 7/8 A+ ½ B
7/8 of A (8) = 7 and ½ of B (6) =3
Together they add up to give hypotenuse to be 7+3=10
*Second* let us try with taking A=28 and B=21 then
by Pythagoras theorem C= √ (21x21+28x28)
C = √ (441+784)
which is =√1225 = 35
According to quatrain : hypotenuse becomes 7/8A + 1/2 B.
7/8 A=7/8 (28) = 24.5 and 1/2B= 1/2 (21) = 10.5
Thus 24.5 + 10.5= 35.
*Third* let us try with taking A= 12 and B= 5 then
By Pythagoras theorem C= √ (12x12) + (5x5) = (144+ 25) √169 =13.
According to the ancient Tamil quatrain : the hypotenuse becomes 7/8A + 1/2B
7/8(12) = 10.5 1/2 (5) = 2.5
Thus 10.5 +2.5 =13
Pothayanar must have been a great mathematician, who got lost like fruit hidden in the foliage of the tree.
The discoveries of the Greek scientists and mathematicians spread far and wide along with their conquests in the world.
Unfortunately, in ancient India, many great intellectuals, and their knowledge / findings were lost to the world owing to various reasons and events.
Our schools teach the Pythagoras Theorem to our children. They should also teach Pothayanar's theorem as an alternate and easier method, as explained above.
Wow Thank you
So fortunate to learn this
May I know where did you find this and where can I find treasures like these?
Thanks again
Doesn’t work with 7,24,25. Or with any right triangle with irrational sides.
It only works for triangles with ratios 3:4:5 and 5:12:13 which is probably why its not commonly used.
Hey, I just heard about the halting problem, so could you help me and everyone else understand? Thanks, Keep making great content!
I remember when I learned this me and my dad had built a shed with a slanted roof and we didn't know how long the top had to be. the next day I walked into my geometry class and told my teacher I had used the Pythagorean theorem on my shed. she was super excited until I said "just kidding I used a tape measure like a normal person." WORTH IT
I think that the fact that the 4 identical right triangles can be arranged into one square in such a way that their hypotenuses make a tilted square is an observation in itself; can't see how that can be taken for granted.
Great explanation better than other videos
pythagorous : i am first to find out this
indian ancients techers : hold my theorem
@Clint Eastwood pls once see ancient books on hindus , everything in maths science etc etc is written there
also i am non-hindu but now i am adopting hinduism
The great Indian mathematician Baudhayana who find Pythagoras theorem first of all other mathematician in the world 🌎🌍.
@1:38 Chinese ancient text mentioned that this relationship was discovered as early as 1000BC. Check on 商高 inside the book called 周髀算經.
Samw for India
Math is really fun. A single theorem can have multiple proofs - as in programming, a problem can have multiple solutions. I remember back in school when we started learning the Pythagorean theorem. The way my teacher used to explain was too boring that if she had explained in such a way that we will use it in our real lives, with showing examples, it would be much more interesting and more students would remember the given information. In fact, one of the best ways to explain mathematics is to visualize them if possible. For me, when I do not understand a proof, or a solution, the best way I will understand it is through graphs which would be kept in my memory for later.
Using Alkashy theorem in right angled triangle 90 having two adjascent sides a and b and the opposite side as c ,c^2 = a^2+ b^2 - 2 a b cos theta as cos 90 is zero and hence a^2+ b^2 = c^2 proving pythsorean theorem.
Pythagoras: i made Pythagorean theorem
Al kashi : hold my Scalar Product