This is a guy who loves his job. It’s clear to see he loves the look on their faces when he blows their minds. I hope to be as happy as him in my working life when I get older
if you learned Pythagoras' theorem in grade 4, you've already learned the prerequisites for it. It doesn't change your ability to teach. How do you think children pick up second languages at a young age faster than the average adult?
howard baxter First year student here. I just love his way of explaining stuff and I can't help but imagine how many more mathematicians we'd see in university if it were taught like this in high school. So many people think they hate math, when in reality it was just taught to them in such a poor way
I’ve used Pythagorean theory in construction almost daily, layout of foundations, roof rafters, staircases. I’ve always known a2+b2=c2, but this guy has explained it so that a 43 yr old carpenter understood it. Nice job mr woo
I'm surprised that he went into such a complex proof, although maybe the math was too advanced for his students. Using his diagram, the total area is (a+b)^2 expanded to a^2 +2ab+b^2.. Adding up the areas of the triangles' area =2ab. Equating the areas yields a*2+2ab+b^2=2ab+c^2. Subtract 2ab from both sides yields a^2+b^2=c^2.
Being a flat earther is more of a thinking process, rather than the belief the earth is flat. Its about not trusting everything you are told at face value but rather using your own logic and perception to discover the world and reality around you and to question the authority that is indoctrinating your psyche. This is a tool that is increasingly being overlooked in traditional western society and hence the need for balance by reinstituting a more critical thinking process. But of course some take it to the extreme and actually think the earth is flat because they themselves can't prove its round
@@ThisIsSolution No, it's not, it's just plain stupidity. Questioning whether the earth is flat or not is a thinking process, but concluding that it is, and thus being a flat earther is just exceedingly stupid, not even worth arguing about. Your definition would fit well on the question of religion though, where the widely accepted idea that some god exists is utter nonsense that has zero proof to back it up.
@@ThisIsSolution Flat eathers reject math and science with the argument but I do not see the earth is round. They reject that planes fly from Australia to the US in 17 hours and about the same to Europe and about the same from Europe to US west coast. If it is flat it means they deliberately would have to waste a lot of money on fuel to keep up the pretend as you would otherwise have to add up some flight times. All to keep up some big conspiracy, a global conspiracy with all the conflicting intetest. Lasting for hundreds of years now. If you cannot understand how stupid that is you are not a critical thinker, you are just dumb. Critical thinkers listen to reason, yes you can believe in government cover ups, you can even make an argument the moon landing was fake, but to say the earth is flat, that just makes you really dumb.
I can’t believe that an incredibly simple concept like the Pythagorean Theorem, one that I’ve been using for countless years, has blown my mind. Goes to show how effective a clever and fun lesson can be.
Im in second year engineering. I've seen this proof countless different ways; but I just can't seem to stop watching the way this guys teaches. It's almost mesmerizing
Senior year university engineering student. Never saw anyone prove this beyond “a^2+b^2=c^2 and it’s just always true because I say it is” until now. This is truly amazing how clearly and explicitly this is explained.
I am a 32 year old moving to a role in forensic collision investigation. I have not used math like this for 15 years and having to re-learn it all. This explanation is fantastic and your enthusiasm with the students is brilliant. Nice work!
I have a degree in mechanical engineering and never learned this, just memorized the equation. I really wish more teachers taught with visual representations, it helps so much.
This video did nothing for me. Seeing it like this doesn’t help. You still have to use the equation. Unless you _need_ to derive it, it’s a waste of time.
@@jacobh674 Okay Jacob. If you can’t see how understanding the way the equation works doesn’t help with comprehension, then I don’t know what to say to you.
The Favourite button could be considered Love I suppose. RUclips needs something other than Like/Dislike it's too polar of an opinion. A full 5 Star system doesn't work either, because most people don't vote like that. So I don't know what would actually work.
theres no purpose of 'favorites" its not a love button. tell me what purpose is it to put a button in your favorite section to see it again later, just search it up, or change the name of favorites to 'stored videos'. A real love button would be like some heart or something that shows how many people love the video, overtly. favorites are like private personal buttons that don't give anything to the uploader
This is one of the most eloquent demonstrations of this proof I've ever seen. Superbly done. It's so especially important too, for such a useful theorem. This is so applicable in so many situations - it's one of the two formulas that I make sure students know before they do an important test like the SAT or ACT, and furthermore can think about how to apply to other shapes or use in combination with trig to figure stuff out.
I think this is the reason why people from Asia usually do better in mathematics than the world population in general. Not only do they just what the formula is but how it is derived. This helps get a better understanding of what math is in instead of learning only some general formulas, which will help later when solving analytical problems in the future.
The fact that so many people are amazed by the fact that the teacher showed visual proof of Pythagoras theorem makes me realise how good of a maths teachers I got in my school.
I find it excellent how this teacher uploads his classes. It has so much benefits to everybody. It makes the students behave, it forces the teacher to give good classes (and hell he does), it gives anyone with an internet connection the ability to attend his classes. I'm glad this channel has 126m subs. Keep it up man, you are a great teacher.
Also coming from a young teacher, it should inspire other teachers to find a way to engage the minds of young people. Maths isn't hard, just need to explain it properly.
3:33 I felt something in my brain just sort of "pop" into place as it finally recognized the polynomial that would reduce to the theorem. The fact that the proof here was then done graphically instead of algebraically is even more beautiful!
This is such a great way to make them understand Pythagoras. Much better than some teachers I know giving students numerical examples to test and to move on
personally for me he explains it way more complicated than just a simle formula. not saying it's a bad thing, but it's easier to memorise a2+b2=c2 and go on. well at least this is the way I did it ~20y ago, had no problem with that and remember till this day. it's a bit concerning how these people will do in uni math class when it will come to matrix or f(x)
+Edd Green, what he does is make them understand the principles behind the formula, instead of memorizing them like our teachers did to us. That's why I am here, I know the formulas, I'm seeking understanding of them, and Eddie Woo's explanations are really satisfying.
Edd Green, by showing the relationship with visuals and also breaking it down bit by bit instead of just giving them the simplified answer, he shows them the thought process behind it. Knowing that thought process can make it easier. My sister had a really hard time understanding x and how to work with it. I, being a year younger had to step in and teach her. If she had Eddie Woo as a teacher, her school life would've been much easier.
Werewolf211, in no way I'm saying Mr.Woo is doing something wrong. I think it's a realy good method if the rest of the teachers would use it, what I'm trying to say is that his students are more likely to strugle in future studies, where will be less engaging methods (e.g. "figure it out yourself" method).
His way of teaching seems thought provoking to me, so I don't see how it'd be a problem. In mathematics of all things, simply following a formula is extremely bad. There are some thing I know how to count, but not why. While my results wouldn't be lacking, it's a horrible thing for future studies. Besides, if you have a better understanding of something, it's also easier to remember. If you can't explain something to someone, you don't understand it well enough.
Very few can we call a true “math teachers” and he is one of them! He is very well engaged with the students and the passion is very present in this lecture! Job well done sir!
Very easy to understand explanation. You are very passionate to teach them the theorem and hence very energetic. This is what makes a teacher a perfect teacher.
At 4:38 the quick solution is to equate the area of the big square to the summation of the area of the triangles and the area of the smaller square. (a+b)² = 4(ab/2)+c². That virtually cuts out the last 7 minutes of the video and cuts right to the proof. a²+2ab+b² = 2ab+c² -->a²+b²=c²
I love how he blows me (who already understands Pythagoras's theorem) away with this amazing example. I have never and most likely would never have looked at it from his perspective. Amazing video, thanks.
My teacher teaching this: Ok here is the Pythagoras' Theorem formula a^2+b^2=c^2 used to solve right triangles. The C side is always the longest side. Now make a right triangle and measure it. Then solve it with this formula making sure to label the long side as C. See, you can solve the longest side without a ruler. Now, open your book and do numbers 1-50. If you don't finish in class, I want it done tomorrow morning. The teacher then sits on her computer for the rest of the class.
Ok like honestly, he has such an engaging way of teaching and he really offers abit of a new perspective on the stuff that I've had to memorise just because I couldnt understand or visualize how they work. His pacing is abit slow, sure but its a good thing cause it gives everyone a chance to be caught up and not left behind and confused like I often am. Great teacher. So much better than the one I have. He is the kind of teacher that would make math fun rather than a headache.
I don't know how i ended up here, but seeing such amazing teachers gives me hope for the future. Please don't give up on your job, and thank you for what you do
Nikolas Tol That’s like me in Geometry... ”Two parallel lines will never touch. What is the rule that says this?” “It’s because the definition of the word ‘parallel’ means they will never touch.” “No, what is the rule that proves it?” *blank* *look* 😐
@@Name-ps9fx technically speaking, parallel line can meat, just not in normal geometry. A somewhat good example of this is a globe. If you take the longitude (the ones that run north and south), there technical definition is that they are parallel at set degree away from the prime meridian at the equator. They are only parallel at the equator do to how they work. They technically not parallel lines (technically sphericalg geometry state no parallel lines exist, but I dont understand spherical geometry enough to understand why. Perhaps they just mean of the lines is as big as the biggest possible straight line). Projected geometry is a lot more complicated, and state that parallel lines intersect, sort of. Basically projected geometry take the fact that the further away something is the smaller and closer to other objects it appears to you. If given infinite eyesight with an infinite flat plane, at some point two infinity long paralle line, no matter how far away from one another, would intersect at a point if you looking at the plane from slightly above it (so your height). This point, the horizon, is called line at infinity and is treated as real as all other points on the plane. All parallel lines meet somewhere on this line, with all non parallel line meeting somewhere on the plane itself. Note that any moving changes the line position (height, rotation, walking, and so on), and extending past this line technically enters spherical geometry (this has been a quick and probably oversimplified version of this problem and projected geometry).
I do have "infinite eye sight". I can see light from as far away as it can travel in sufficient quantity and intensity for my eyes to perceive. For instance I can see stars that are billions of miles away. Yet I may not be able to see a candle a few miles away.
It's a square because that is what "we" have all agreed to call a shape with 4 equal sides and a 90 degree right angle. If "we all" agreed to call it a triangle then that's what it would be. And the shape that we currently call a triangle "we all" could agree to call a square. And so that is what they would be.
It's like watching a magic show. Confusing yet mesmerising Simple yet mind blowing Edit : I've got it. He's a *mathmagician* ....I'll let myself out now...
I learned Pythagoras' Theorem without actually learning it.. I'm realizing this now at 25 years old. You are an incredible teacher, and the way you allow these students to see what's actually happening is just fantastic and I'm jealous of them
Awesome teacher! Many moons ago when I was in geometry I learned the theorem but I did not learn it visually as you taught it. Very cool ! Keep up the good work sir, we nrry great teachers like you... Your energy and enthusiasm keeps them interested, and I love how you make it interactive with them rather than just lecture.
this really demonstrates the difference between a person who learns to teach, and a person who learns a discipline, then teaches it. We have too many 'teachers' in our schools. We need more 'masters of subject' who then decide to teach. masters can explain topics articulately and in simple terms. and that helps students.
Mr Woo, if you happened to read this then listen up...u are the best of them all.. Ur work is great and I'm so lucky that I've got a chance to learn from such a wonderful teacher like u.. I anyway liked math, but u made me love math..I'm so happy..☺🙂
If you make the class exiting, you dont have to worry about the students not behaving, because they listen to you because you make it exciting. Amazing to see this teacher.
professor woo, gcse student here, you're helping us all over the world, and it's great to see your interest in mathematics and hopefully we'll all cultivate the same interest for it as you do with time. thanks eddie woo!
Ooohhh my godd!! This was just woww!! The teacher's expression his interest showed how happy he was teaching his students.... Best part was that he just not made them mug up the formulae and the way the student shouted the answer showed their interest too 🤩🤩
I really liked the amount of engagement this teacher fostered within me in just 10mins. I am an average student. The only reason I was topper during primary school was that none of the math was ever hard. But in middle school the real math hit me. On top of that, the pandemic restricted in-person classes for almost 2 years. Which means my entire 7th and 8th grade went to waste. Our 8th-grade finals were conducted in school and I did not do well in subjects like math, chemistry and computer, my weaker subjects. Except for those, my grades have been more or so alright. Based on the book I got from my seniors we have Pythagoras theorem from 9th grade onwards. I wanted to cultivate an interest in Math. Therefore I am glad I found this teacher. In my school teachers only did the exercises and never told us how it was formed in the first place. If we were unable to understand or do some sums we were expected to go to extra tuition and take help from the teachers. The tuitions were never any better than the schools. The same students would reach home after 6 hours of schooling and then go through 5-6 hours of tuition. No real engagement or interest. As someone with a lot of visual ability, excelling in arts and creativity, I came to know how visually studying benefited me. As I am starting high school I hope to reach greater heights and be more than an average student.
Thanks so much! I'm doing my Year 8 Ignite currently and we just learnt about congruence, transformations, and proofing and this helps so much for later on this year!
This is brilliant, time and time again its shown that people remember these more easily when they understand WHY something happens. I of course learned this in school but no one ever showed me this way of showing WHY a squared + b squared = c squared.
Fantastic way to teach. This is how every teacher should teach. Congratulations and THANK YOU for being such an example as a teacher. It's quite strange why people with no devotion to teach choose to be teacher. Mr. Eddie Woo is one of a kind, he is a TRULY Teacher.
Hes such a great teacher while my teacher dosen't show examples physically as he does. But my old teacher makes us go on to our school devices everytime.
I'm forty eight years old, and I had A teacher in middle school that you remind me of. I often think about him, and how incredible he was. You sir are just as incredible, and the impact you are making on these kids lives is beautiful, and lifelong! God bless.
I loved this visual explanation. I love how he broke down each step. He clearly has energy, involves the class, and loves explaining. One thing I wish he explained: how do we know for certain that the c,c,c,c shape in the middle is definitely a square? Is it because we know that if all sides are the same it's automatically a square?
If you're asking the question for yourself, then: We know that all three inner angles of any triangle add up to 180° and that a right angle is 90°. So taking the right angle away from the total, the other two angles add to 90°. We know that a straight line is 180°, so in those corners of the inner square where the two triangles touch, 180° of the straight line minus the two angles (that add to 90°) equals 90°, which is the same for each corner because they're the same triangles we started with. Combine that with knowing the sides are all C, and that defines a square.
This guy takes his job fun and seriously making sure every single student understands his word while interacting with them KEEP IT UP P.S. we need more people like you
I have my exams a month later and in maths, Pythagoras Theorem is one of the chapters. I have already understood it but now i'll see the video to see if I can understand it better.
When my high school biology teacher demonstrated what a macrophage was by eating her stub of chalk, I never forgot what a macrophage was. There are teachers and then there are teachers.
Eddie...I hated math in high school...but after watching your TED talk, I'm going to go through every one of your videos and start from the beginning again!
They are also known as Pythagorean ternas, and another one it's: 8^2 + 6^2 = 10^2 But I see why the first one it's very particular, as far as I'm aware it's the only one which contains consecutive numbers, as the group of 3,5 and 7, the only group of primes which are separated by two units. (well..it's the only known curently)
You actually don't need the second square configuration. Having established the side length of the square as a+b, there are, in fact, 2 ways to write the area. First is traditional area of a square [(a+b)^2]. Second is adding the area of the shapes that made it [4x triangle (ab/2) + square C (c^2)]. We can equate these areas to give the following: (a+b)^2=4(ab/2)+c^2 Expanding: a^2+2ab+b^2=2ab+c^2 Subtract 2ab from both sides: a^2+b^2=c^2 QED
You could also give an area argument (without having to apply transformations), noting that the total area of the larger square is (a+b)^2 and that the area of just the green portion is 2ab. From here, we know the area of the inner square is a^2 + b^2, so the length of each side of the inner square is sqrt(a^2 + b^2). The Pythagorean theorem follows since each side of the inner square is the hypotenuse of each triangle.
@@vladislavkucher2718 Oh did be give that alternate proof at some point? My proof is slightly different since it doesn't require any translations and formations of new shapes.
@@FireSwordOfMagic You can use side-angle-side criterion for the congruence and do not mention any movements. But since he cut all triangles from the paper he may enjoy using them.
It's one thing to know Pythagoras' Theorem, but another to actually visualize it and understand why it works. This was pretty cool to watch, and I wish my teachers when I was in school had taught it this way, instead of saying "here's a formula, now memorize it."
Usually when lines rotate they form surfaces. So rotation and translation. Rotation is multiple and translation is add or subtract. So surfaces equals other because of equal rotational symmetry. So integration is some form of rotational symmetry. Essentially when you do integration you are finding the rotational symmetry of numbers. Prime act as vortex.
But before rearranging it, couldn't you do (a+b)^2 for the entire area of the square, which is a^2+b^2+2ab, which then has to equal the 4 triangles *AND* c^2? So to figure out the 4 triangle areas, its 4ab/2 = 2ab. So, a^2+b^2+2ab = 4ab/2+c^2 which 4ab/2 is 2ab so a^2+b^2+2ab = 2ab+c^2. Subtracting 2ab from both sides gives you a^2+b^2 = c^2.
good try on pretending to be genius but sorry you failed unless you record a video of your own. people failed math because most of them had teachers like you, who could only able to intepret using whole bunch of words which complicate things. just look at those a's and b's in your original comment, honestly i wouldn't give a fuck if my teacher taught me the theorem in your way.
of course you could. There are various ways to prove the theorem. But the point is. In order to do that, you need to have learned already how to calculate ( a + b ) ^ 2. I know, this is not hard. But yet. You need to know how to do it, which might not be the case for this kids. His goal was to present an entirely graphical prove. All that is needed is to know how to actually calculate the area of a rectangle given its (simple - that is 1 "letter") side length and by paying attention. Nothing more is needed. The rest is just recognizing that the 4 green rectangles in the first "big square" and in the second figure are the same (just rearranged) and thus can be removed from either figure, leaving you in the first case with the blue suare (representing c^2) and leaving you in the second case with 2 smaller squares representing a^2 and b^2.
have always been memorising only. and this is how a teacher teaching with passion blows a 30 years old engineer's mind having to rediscover again a secondary school lesson.
im currently taking integral calculus and here i am, watching shapes and colors. explained so beautifully and eloquently. i wish i had that growing up. thank you for this
This tcr is unlike the others. What makes him so good is that he has every justifications to every maths theory. He makes us understand what is is and how it works. Unlike other tcr where they just give us the formula and that's about it
Love it but I think an additional clarity was needed for the final proof. "The big square did not change size so subtracting the green triangles from it give us the exact same thing now as it did before".
Our geometry teacher gave us this as an assignment in high school. He gave us the theorem (with no explanation, in the pre-internet era), and 1 week to prove it. Up to today I Still remember the feeling when I figured it out (and that's a few decades away), even though I couldn't do it anymore. Great to see him explain it, got that same rush when it clicked. Definitely gonna help my kids figure this one out themselves, because it us the best way to remember it forever ánd boost your confidence.
I think pink and yellow square make things more complicated, I think you can get C2 with the big area which is (a+b)(a+b) and substract it with the area of 4 triangle (4x1/2ab) hence (a+b)(a+b)-(2ab) = c2 and then simplified it to a2+2ab+b2-2ab = c2 then you can just substract 2ab and 2ab so it leave a2+b2=c2
I love how he took the time to break it down to show the proof is not a load of tosh. Far better than when I was in school and the teacher just drawing the a² + b² = c² in the board and using a metre stick to draw the “famous” ones towards the end. I wish I had more teachers like him. And through RUclips I can. I don’t need to be a child with time machine. You always learn and today I learnt more in these eleven minutes than that forty odd minute class, those 𝑥 years ago!
4:29 area of bigger square is (a+b)^2 And inner one is c^2 so the leftover, area of four triangles must be (a+b)^2-c^2..... And we know area of those triangles is 4 times ab/2. So(a^2 + b^2 +2ab) - c ^2= 4(ab/2) a^2 + b^2 - c^2=2ab-2ab=0 a^2 + b^2 =c^2
I honestly can't wait to watch the rest of this channel's videos.Both well done and the enthusiasm made me smile. Apparently 1.2K people are still smoking outside shop class though.
I don't know why but watching this makes me a bit emotional! I wish someone taught me PT this way 20 years ago when I was at school. I was terrible at Maths Methods and I don't think I ever fully grasped even the basics of PT. This video has helped me understand the fundamentals in 11 mins.
This is the best way to teach Pythagoras to kids. I would suggest two better ways to show left over squares a^2 and b^2 from 5:45: a. Use like what Euclid did. The green triangles slide to the opposite sides. b. to convince students that the first big square with a hole in the middle is the same with the latest square after moving/rotating two of the green triangles, that in 5:53 the bottom left triangle should be rotated to the right (pivot in the same contact point), instead of, like what you did, rotating the bottom right to the left. Then give two dot signs on the corner top left and right bottom to show that the same imaginary square is still intact. So, no need to move the new green rectangle at the bottom to the right and to convince the students about it that the new side lengths are the same, b+a and a+b.
This is a guy who loves his job. It’s clear to see he loves the look on their faces when he blows their minds. I hope to be as happy as him in my working life when I get older
Obviously easy when you have to explain it to much older people. We learned this in 4th grade. Try to teach it there.
if you learned Pythagoras' theorem in grade 4, you've already learned the prerequisites for it. It doesn't change your ability to teach. How do you think children pick up second languages at a young age faster than the average adult?
Hell yeah i'd love to have such a teacher
Absolutely some people are extremely lucky doing what they love...
me i wish only to study in his class
What am I doing? I finished calculus 3 years ago. These videos are just so pleasing to watch!
LMAO I'm a Master's Student in Mathematics and I'm still watching this stuff!
Lol, I’m a freshman in college relearning Calc 3. It’s always good to go back to the basics.
howard baxter First year student here. I just love his way of explaining stuff and I can't help but imagine how many more mathematicians we'd see in university if it were taught like this in high school. So many people think they hate math, when in reality it was just taught to them in such a poor way
I have a PhD in Mathematics and I'm watching this:D
Which field?
I’ve used Pythagorean theory in construction almost daily, layout of foundations, roof rafters, staircases. I’ve always known a2+b2=c2, but this guy has explained it so that a 43 yr old carpenter understood it. Nice job mr woo
Same here. I never really understood it, but now I finally do.
Have you ever used a hollow plastic (flexible) tube filled with water to determine the levelness of two distant points (before lasers)?
That's what I can expect from you, yes you
100%!!
I'm surprised that he went into such a complex proof, although maybe the math was too advanced for his students. Using his diagram, the total area is (a+b)^2 expanded to a^2 +2ab+b^2.. Adding up the areas of the triangles' area =2ab. Equating the areas yields a*2+2ab+b^2=2ab+c^2. Subtract 2ab from both sides yields a^2+b^2=c^2.
I bet you none of his students ever became a flat-earther
Underrated lol
😂😂😂😂
Being a flat earther is more of a thinking process, rather than the belief the earth is flat.
Its about not trusting everything you are told at face value but rather using your own logic and perception to discover the world and reality around you and to question the authority that is indoctrinating your psyche.
This is a tool that is increasingly being overlooked in traditional western society and hence the need for balance by reinstituting a more critical thinking process. But of course some take it to the extreme and actually think the earth is flat because they themselves can't prove its round
@@ThisIsSolution No, it's not, it's just plain stupidity. Questioning whether the earth is flat or not is a thinking process, but concluding that it is, and thus being a flat earther is just exceedingly stupid, not even worth arguing about. Your definition would fit well on the question of religion though, where the widely accepted idea that some god exists is utter nonsense that has zero proof to back it up.
@@ThisIsSolution
Flat eathers reject math and science with the argument but I do not see the earth is round.
They reject that planes fly from Australia to the US in 17 hours and about the same to Europe and about the same from Europe to US west coast. If it is flat it means they deliberately would have to waste a lot of money on fuel to keep up the pretend as you would otherwise have to add up some flight times. All to keep up some big conspiracy, a global conspiracy with all the conflicting intetest. Lasting for hundreds of years now.
If you cannot understand how stupid that is you are not a critical thinker, you are just dumb. Critical thinkers listen to reason, yes you can believe in government cover ups, you can even make an argument the moon landing was fake, but to say the earth is flat, that just makes you really dumb.
"The mediocre teacher tells. The good teacher explains. The superior teacher demonstrates. The great teacher inspires" - - William Arthur Ward
ClassyAF woahhhhh
This comment has 99 likes. Now I am forced to make it 100 coz I can't handle that
When I heard William Arthur my mind went somewhere else for sometime
and the bad teacher always compares you with the topper
This guy is one of those four...
I can’t believe that an incredibly simple concept like the Pythagorean Theorem, one that I’ve been using for countless years, has blown my mind. Goes to show how effective a clever and fun lesson can be.
Im in second year engineering. I've seen this proof countless different ways; but I just can't seem to stop watching the way this guys teaches. It's almost mesmerizing
Asian + passion + funny English accent = ASMR
That's an Australian accent.
I am in grade 11 scientific, my math teacher can't prove it
I asked him and he didn't know. My grade 8 teacher was able to prove it 10 different times
Senior year university engineering student. Never saw anyone prove this beyond “a^2+b^2=c^2 and it’s just always true because I say it is” until now. This is truly amazing how clearly and explicitly this is explained.
"It's a square."
"I kn-I'm trying to SHOW that it's a sqaure!"
3:03 wow
I am a 32 year old moving to a role in forensic collision investigation. I have not used math like this for 15 years and having to re-learn it all. This explanation is fantastic and your enthusiasm with the students is brilliant. Nice work!
I have a degree in mechanical engineering and never learned this, just memorized the equation. I really wish more teachers taught with visual representations, it helps so much.
This video did nothing for me. Seeing it like this doesn’t help. You still have to use the equation. Unless you _need_ to derive it, it’s a waste of time.
@@jacobh674 its just visual proof, it says in the title. It helps with understanding how it works as well though.
@@jacobh674 Okay Jacob. If you can’t see how understanding the way the equation works doesn’t help with comprehension, then I don’t know what to say to you.
@@jacobh674 This isn’t the flex that you think it is.
@@officerwizz His visual proof help me understand everything. Instead of just memorizing the equation.
It's teachers like this that capture imaginations and inspire a generation.
I hope he and others like him never lose their passion.
why doesn't YT have a 'love' button yet?
its called sub XD
The Favourite button could be considered Love I suppose. RUclips needs something other than Like/Dislike it's too polar of an opinion. A full 5 Star system doesn't work either, because most people don't vote like that. So I don't know what would actually work.
that's what your 'favorites' playlist is for. after all, the like button is just a "add to liked videos" button
theres no purpose of 'favorites" its not a love button. tell me what purpose is it to put a button in your favorite section to see it again later, just search it up, or change the name of favorites to 'stored videos'. A real love button would be like some heart or something that shows how many people love the video, overtly. favorites are like private personal buttons that don't give anything to the uploader
There's no 'love' button because YT is too toxic & no one knows how to loving-hearted - in fact it's impossible
This is one of the most eloquent demonstrations of this proof I've ever seen. Superbly done. It's so especially important too, for such a useful theorem. This is so applicable in so many situations - it's one of the two formulas that I make sure students know before they do an important test like the SAT or ACT, and furthermore can think about how to apply to other shapes or use in combination with trig to figure stuff out.
I think this is the reason why people from Asia usually do better in mathematics than the world population in general. Not only do they just what the formula is but how it is derived. This helps get a better understanding of what math is in instead of learning only some general formulas, which will help later when solving analytical problems in the future.
The fact that so many people are amazed by the fact that the teacher showed visual proof of Pythagoras theorem makes me realise how good of a maths teachers I got in my school.
How does your teacher teach? Would be nice if he or she started a RUclips channel too
I’ve got a degree in math and I’ve never seen anything like this.
@@soundpreacher me being a student who never saw this
Same. I got this EXACT lesson from my Maths Teacher, I'm nearly sure she must have watched this video
I find it excellent how this teacher uploads his classes. It has so much benefits to everybody.
It makes the students behave, it forces the teacher to give good classes (and hell he does), it gives anyone with an internet connection the ability to attend his classes. I'm glad this channel has 126m subs. Keep it up man, you are a great teacher.
Also coming from a young teacher, it should inspire other teachers to find a way to engage the minds of young people. Maths isn't hard, just need to explain it properly.
gorillaau i think what u say is true, maths is not HARD but just very mystic and un instinctual for most people
3:33 I felt something in my brain just sort of "pop" into place as it finally recognized the polynomial that would reduce to the theorem. The fact that the proof here was then done graphically instead of algebraically is even more beautiful!
This is such a great way to make them understand Pythagoras. Much better than some teachers I know giving students numerical examples to test and to move on
personally for me he explains it way more complicated than just a simle formula. not saying it's a bad thing, but it's easier to memorise a2+b2=c2 and go on. well at least this is the way I did it ~20y ago, had no problem with that and remember till this day. it's a bit concerning how these people will do in uni math class when it will come to matrix or f(x)
+Edd Green, what he does is make them understand the principles behind the formula, instead of memorizing them like our teachers did to us. That's why I am here, I know the formulas, I'm seeking understanding of them, and Eddie Woo's explanations are really satisfying.
Edd Green, by showing the relationship with visuals and also breaking it down bit by bit instead of just giving them the simplified answer, he shows them the thought process behind it. Knowing that thought process can make it easier.
My sister had a really hard time understanding x and how to work with it. I, being a year younger had to step in and teach her. If she had Eddie Woo as a teacher, her school life would've been much easier.
Werewolf211, in no way I'm saying Mr.Woo is doing something wrong. I think it's a realy good method if the rest of the teachers would use it, what I'm trying to say is that his students are more likely to strugle in future studies, where will be less engaging methods (e.g. "figure it out yourself" method).
His way of teaching seems thought provoking to me, so I don't see how it'd be a problem. In mathematics of all things, simply following a formula is extremely bad. There are some thing I know how to count, but not why. While my results wouldn't be lacking, it's a horrible thing for future studies. Besides, if you have a better understanding of something, it's also easier to remember.
If you can't explain something to someone, you don't understand it well enough.
Very few can we call a true “math teachers” and he is one of them! He is very well engaged with the students and the passion is very present in this lecture! Job well done sir!
Very easy to understand explanation. You are very passionate to teach them the theorem and hence very energetic. This is what makes a teacher a perfect teacher.
Don’t forget he teaches it clearly
Hence a very 'easy to understand' explanation 😉
Bugra Engin Oh yeah I guess I read over that
At 4:38 the quick solution is to equate the area of the big square to the summation of the area of the triangles and the area of the smaller square. (a+b)² = 4(ab/2)+c². That virtually cuts out the last 7 minutes of the video and cuts right to the proof. a²+2ab+b² = 2ab+c² -->a²+b²=c²
@@JSSTyger
It simplifies it.
This guy is just a great teacher. The way he explains, his interaction with the students and his enthusiasm are A1.
I love how he blows me (who already understands Pythagoras's theorem) away with this amazing example. I have never and most likely would never have looked at it from his perspective. Amazing video, thanks.
My teacher teaching this:
Ok here is the Pythagoras' Theorem formula a^2+b^2=c^2 used to solve right triangles. The C side is always the longest side. Now make a right triangle and measure it. Then solve it with this formula making sure to label the long side as C. See, you can solve the longest side without a ruler.
Now, open your book and do numbers 1-50. If you don't finish in class, I want it done tomorrow morning.
The teacher then sits on her computer for the rest of the class.
I love the flow of thoughts displayed by Eddie.when Passion meets with knowledge ,great things happen. Have learnt a skill as a math teacher.
Ok like honestly, he has such an engaging way of teaching and he really offers abit of a new perspective on the stuff that I've had to memorise just because I couldnt understand or visualize how they work. His pacing is abit slow, sure but its a good thing cause it gives everyone a chance to be caught up and not left behind and confused like I often am. Great teacher. So much better than the one I have. He is the kind of teacher that would make math fun rather than a headache.
I don't know how i ended up here, but seeing such amazing teachers gives me hope for the future. Please don't give up on your job, and thank you for what you do
Eddie: Why is it a square?
Kid: Because it is a square.
That kid is a genius!!
Nikolas Tol
That’s like me in Geometry...
”Two parallel lines will never touch. What is the rule that says this?”
“It’s because the definition of the word ‘parallel’ means they will never touch.”
“No, what is the rule that proves it?”
*blank* *look* 😐
@@Name-ps9fx technically speaking, parallel line can meat, just not in normal geometry. A somewhat good example of this is a globe. If you take the longitude (the ones that run north and south), there technical definition is that they are parallel at set degree away from the prime meridian at the equator. They are only parallel at the equator do to how they work. They technically not parallel lines (technically sphericalg geometry state no parallel lines exist, but I dont understand spherical geometry enough to understand why. Perhaps they just mean of the lines is as big as the biggest possible straight line).
Projected geometry is a lot more complicated, and state that parallel lines intersect, sort of. Basically projected geometry take the fact that the further away something is the smaller and closer to other objects it appears to you. If given infinite eyesight with an infinite flat plane, at some point two infinity long paralle line, no matter how far away from one another, would intersect at a point if you looking at the plane from slightly above it (so your height). This point, the horizon, is called line at infinity and is treated as real as all other points on the plane. All parallel lines meet somewhere on this line, with all non parallel line meeting somewhere on the plane itself. Note that any moving changes the line position (height, rotation, walking, and so on), and extending past this line technically enters spherical geometry (this has been a quick and probably oversimplified version of this problem and projected geometry).
Holyshit
I do have "infinite eye sight". I can see light from as far away as it can travel in sufficient quantity and intensity for my eyes to perceive. For instance I can see stars that are billions of miles away. Yet I may not be able to see a candle a few miles away.
It's a square because that is what "we" have all agreed to call a shape with 4 equal sides and a 90 degree right angle. If "we all" agreed to call it a triangle then that's what it would be. And the shape that we currently call a triangle "we all" could agree to call a square. And so that is what they would be.
I finally understand the Pythagoras Theorem. This guy is a great teacher. The school and the students are really lucky to have him as teacher.
It's like watching a magic show.
Confusing yet mesmerising
Simple yet mind blowing
Edit : I've got it. He's a *mathmagician*
....I'll let myself out now...
Your imagination is great. Simple yet complex.
You're an imagician 🥳
*mathemagician
That said it all. It was truth, with an equal sided triangle for me completely. Math is magic, math, mind blowing and art at the same time!
how is this confusing? it's gotta be like the easiest way to explain pythagoras theorem
@@nabulodonozor LOL ikr xD
I learned Pythagoras' Theorem without actually learning it.. I'm realizing this now at 25 years old. You are an incredible teacher, and the way you allow these students to see what's actually happening is just fantastic and I'm jealous of them
Awesome teacher! Many moons ago when I was in geometry I learned the theorem but I did not learn it visually as you taught it. Very cool ! Keep up the good work sir, we nrry great teachers like you... Your energy and enthusiasm keeps them interested, and I love how you make it interactive with them rather than just lecture.
this really demonstrates the difference between a person who learns to teach, and a person who learns a discipline, then teaches it. We have too many 'teachers' in our schools. We need more 'masters of subject' who then decide to teach. masters can explain topics articulately and in simple terms. and that helps students.
I’m very lucky my history teacher teaches a lot like this guy and I love her class.
Why can’t this guy be my pre-calc teacher this year!! He’s so good at teaching!!
Mr Woo, if you happened to read this then listen up...u are the best of them all.. Ur work is great and I'm so lucky that I've got a chance to learn from such a wonderful teacher like u.. I anyway liked math, but u made me love math..I'm so happy..☺🙂
I am glad for you :) With a teacher like that I would have understood much more about math
If you make the class exiting, you dont have to worry about the students not behaving, because they listen to you because you make it exciting. Amazing to see this teacher.
That kid who said 25 , if you're reading this I want you to know you're awesome
No he's not, sounded like a prick
ohh yesssss....he is so cute really.....
that kid who said 25 is stupid if he thinks shouting out 25 is him being so cool as to knowing what 5 squared is.
No he thinks he's a genius for knowing what 5 squared is
@@Dan-jp2th give him a break he's just a kid you said it yourself
professor woo, gcse student here, you're helping us all over the world, and it's great to see your interest in mathematics and hopefully we'll all cultivate the same interest for it as you do with time. thanks eddie woo!
What a great teacher, awesome spirit, energy and kindness! Hopefully he cann keep it long and doesnt get demotivated by the system!
“Algebra doesn’t care” 😂
Ooohhh my godd!! This was just woww!! The teacher's expression his interest showed how happy he was teaching his students.... Best part was that he just not made them mug up the formulae and the way the student shouted the answer showed their interest too 🤩🤩
i love this guys energy teaching, my teachers didnt have that at school not even a bit of it. luckily math was exiting enough to keep me interested.
Pity your English teacher wasn't so exciting.... notice the spelling... exiting = exciting... :)
I really liked the amount of engagement this teacher fostered within me in just 10mins. I am an average student. The only reason I was topper during primary school was that none of the math was ever hard. But in middle school the real math hit me. On top of that, the pandemic restricted in-person classes for almost 2 years. Which means my entire 7th and 8th grade went to waste. Our 8th-grade finals were conducted in school and I did not do well in subjects like math, chemistry and computer, my weaker subjects. Except for those, my grades have been more or so alright.
Based on the book I got from my seniors we have Pythagoras theorem from 9th grade onwards. I wanted to cultivate an interest in Math. Therefore I am glad I found this teacher. In my school teachers only did the exercises and never told us how it was formed in the first place. If we were unable to understand or do some sums we were expected to go to extra tuition and take help from the teachers. The tuitions were never any better than the schools. The same students would reach home after 6 hours of schooling and then go through 5-6 hours of tuition. No real engagement or interest. As someone with a lot of visual ability, excelling in arts and creativity, I came to know how visually studying benefited me.
As I am starting high school I hope to reach greater heights and be more than an average student.
Here I am in AP Calculus BC as a junior, actually learning what Pythagorean’s theorem is. I love this guy, thank you.
bruh this theorem is so easy to understand wdym lol
Thanks so much! I'm doing my Year 8 Ignite currently and we just learnt about congruence, transformations, and proofing and this helps so much for later on this year!
And everyone actually learned in that day.
This is brilliant, time and time again its shown that people remember these more easily when they understand WHY something happens. I of course learned this in school but no one ever showed me this way of showing WHY a squared + b squared = c squared.
10:41 I love how he says "very good" to that kid who says 25
Fantastic way to teach. This is how every teacher should teach. Congratulations and THANK YOU for being such an example as a teacher.
It's quite strange why people with no devotion to teach choose to be teacher. Mr. Eddie Woo is one of a kind, he is a TRULY Teacher.
Great teacher! I like watching his videos and will show them also to my kids as they grow ;) Keep on Eddie! Thanks so much!
This is the kind of math teacher I would have loved to have in my school years. I have no doubt I wouldn’t have dislike/hate math as I did back then.
Hes such a great teacher while my teacher dosen't show examples physically as he does. But my old teacher makes us go on to our school devices everytime.
I'm forty eight years old, and I had A teacher in middle school that you remind me of. I often think about him, and how incredible he was. You sir are just as incredible, and the impact you are making on these kids lives is beautiful, and lifelong! God bless.
I loved this visual explanation. I love how he broke down each step. He clearly has energy, involves the class, and loves explaining.
One thing I wish he explained: how do we know for certain that the c,c,c,c shape in the middle is definitely a square? Is it because we know that if all sides are the same it's automatically a square?
If you're asking the question for yourself, then:
We know that all three inner angles of any triangle add up to 180° and that a right angle is 90°. So taking the right angle away from the total, the other two angles add to 90°. We know that a straight line is 180°, so in those corners of the inner square where the two triangles touch, 180° of the straight line minus the two angles (that add to 90°) equals 90°, which is the same for each corner because they're the same triangles we started with. Combine that with knowing the sides are all C, and that defines a square.
why i didn't get a maths teacher like him?
answer: i am not lucky.
Nothing to do with luck. There are many Maths teachers out there who just love Maths and get excited by numbers. It's up to you to find one.
believe ur self man and be smart
Mr.Mister yeah go find one. Mom I wanna keep changing schools untill I find a good math teacher!
Okay sweety.
No.
what a way to explain Pythagoras theorem. great teaching
This guy takes his job fun and seriously making sure every single student understands his word while interacting with them
KEEP IT UP
P.S. we need more people like you
I have my exams a month later and in maths, Pythagoras Theorem is one of the chapters. I have already understood it but now i'll see the video to see if I can understand it better.
When my high school biology teacher demonstrated what a macrophage was by eating her stub of chalk, I never forgot what a macrophage was.
There are teachers and then there are teachers.
Mind blown!
AussiB it's hard to understand or what?
Eddie...I hated math in high school...but after watching your TED talk, I'm going to go through every one of your videos and start from the beginning again!
They are also known as Pythagorean ternas, and another one it's:
8^2 + 6^2 = 10^2
But I see why the first one it's very particular, as far as I'm aware it's the only one which contains consecutive numbers, as the group of 3,5 and 7, the only group of primes which are separated by two units. (well..it's the only known curently)
Karen Sarai Morales Montiel you just doubled the one he used. The simplest form of yours is still 3^2+4^2=5^2
it's not possible to have any other pythagorean triple with consecutive numbers... it's not hard to work out and prove it. ie 3,4,5 is the only group.
You actually don't need the second square configuration. Having established the side length of the square as a+b, there are, in fact, 2 ways to write the area. First is traditional area of a square [(a+b)^2]. Second is adding the area of the shapes that made it [4x triangle (ab/2) + square C (c^2)]. We can equate these areas to give the following:
(a+b)^2=4(ab/2)+c^2
Expanding:
a^2+2ab+b^2=2ab+c^2
Subtract 2ab from both sides:
a^2+b^2=c^2
QED
My teacher's aren't like him that's why I'm here❣️🔥
You could also give an area argument (without having to apply transformations), noting that the total area of the larger square is (a+b)^2 and that the area of just the green portion is 2ab. From here, we know the area of the inner square is a^2 + b^2, so the length of each side of the inner square is sqrt(a^2 + b^2). The Pythagorean theorem follows since each side of the inner square is the hypotenuse of each triangle.
You just repeat what he said :)
@@vladislavkucher2718 Oh did be give that alternate proof at some point? My proof is slightly different since it doesn't require any translations and formations of new shapes.
@@FireSwordOfMagic You can use side-angle-side criterion for the congruence and do not mention any movements. But since he cut all triangles from the paper he may enjoy using them.
10:25 i like this kid in the video . These kids must be encouraged . He is very energetic kid and he is happy . TWENTY - FIVE
It’s so fascinating that the left over triangles that form 2 rectangles are 2ab from (a+b)^2 that equals a^2 + 2ab + b^2, so fascinating I love maths
*"But how do you kNouuuuuwww it's a square?"*
What a great explanation of Pythagorean Theorem. This dude was born to be an instructor.
8:42 was the moment I remembered the blue square was c×c and I knew where it was going
It's one thing to know Pythagoras' Theorem, but another to actually visualize it and understand why it works. This was pretty cool to watch, and I wish my teachers when I was in school had taught it this way, instead of saying "here's a formula, now memorize it."
9:56 When the realisation kicks in.
In my teacher's opinion I'm too young to understand ur explanation but I really understand every single word u say ❤❤ keep on this wonderful work 💙💙
What an awesome teacher!!! Need more of this. And! Need to reward teachers like this financially!
25!!!!!! XD that kid so desperate to answer
What an amazing teacher... What a beautiful teaching style... Hats off
Usually when lines rotate they form surfaces. So rotation and translation. Rotation is multiple and translation is add or subtract. So surfaces equals other because of equal rotational symmetry. So integration is some form of rotational symmetry. Essentially when you do integration you are finding the rotational symmetry of numbers. Prime act as vortex.
52…Hardly ever use geometry, but you are an EXCELLENT teacher and now I have to watch all your videos. Well done.
But before rearranging it, couldn't you do (a+b)^2 for the entire area of the square, which is a^2+b^2+2ab, which then has to equal the 4 triangles *AND* c^2? So to figure out the 4 triangle areas, its 4ab/2 = 2ab.
So, a^2+b^2+2ab = 4ab/2+c^2 which 4ab/2 is 2ab so a^2+b^2+2ab = 2ab+c^2.
Subtracting 2ab from both sides gives you a^2+b^2 = c^2.
good try on pretending to be genius but sorry you failed unless you record a video of your own. people failed math because most of them had teachers like you, who could only able to intepret using whole bunch of words which complicate things. just look at those a's and b's in your original comment, honestly i wouldn't give a fuck if my teacher taught me the theorem in your way.
@@whyahh the fuck? I'm not a teacher, I'm a dude who likes math. I'm just pointing something out, not tryna be genius
of course you could. There are various ways to prove the theorem.
But the point is. In order to do that, you need to have learned already how to calculate ( a + b ) ^ 2.
I know, this is not hard. But yet. You need to know how to do it, which might not be the case for this kids.
His goal was to present an entirely graphical prove. All that is needed is to know how to actually calculate the area of a rectangle given its (simple - that is 1 "letter") side length and by paying attention. Nothing more is needed. The rest is just recognizing that the 4 green rectangles in the first "big square" and in the second figure are the same (just rearranged) and thus can be removed from either figure, leaving you in the first case with the blue suare (representing c^2) and leaving you in the second case with 2 smaller squares representing a^2 and b^2.
@@kellyhe3012 there are atleast 3 or 4 ways to visually prove . What you said is one of them. Quit trying to be smart.
@@robertlee-nq6mg lmao pythagorean theorem is smart ok hon
have always been memorising only. and this is how a teacher teaching with passion blows a 30 years old engineer's mind having to rediscover again a secondary school lesson.
Isn't he the coolest teacher ?
I love math , but i wish I had this guy as my teacher because I feel his instruction would have helped me succeed to a higher level .
im currently taking integral calculus and here i am, watching shapes and colors. explained so beautifully and eloquently. i wish i had that growing up. thank you for this
His style of teaching is very good!! I like him. From now I may start taking lessons from his videos.
This tcr is unlike the others. What makes him so good is that he has every justifications to every maths theory. He makes us understand what is is and how it works. Unlike other tcr where they just give us the formula and that's about it
Why don’t I have a math teacher like that 😂!!!!
I knew a2 + b2 = c2 but I never saw it explained in this very visual way. Man, I’m 67 now and still learning. Thank you Eddie.
I wonder what grade is this
hahahah ...
I wonder too...
Considering this is a British school, I don’t know. In America they would likely be in 8th or 9th grade (7th for some).
howard baxter they are Australian not British
howard baxter this isn't British
4th year (year 11)
If you live in a domicile, this theorem is how it stays standing.
3,4,5 triangle is how you know what you're building is square.
Fantastic teacher, attracts attention.
Love it but I think an additional clarity was needed for the final proof. "The big square did not change size so subtracting the green triangles from it give us the exact same thing now as it did before".
Our geometry teacher gave us this as an assignment in high school. He gave us the theorem (with no explanation, in the pre-internet era), and 1 week to prove it.
Up to today I Still remember the feeling when I figured it out (and that's a few decades away), even though I couldn't do it anymore. Great to see him explain it, got that same rush when it clicked.
Definitely gonna help my kids figure this one out themselves, because it us the best way to remember it forever ánd boost your confidence.
So helpful! Also those kids competing to shout the multiplication answers first definitely brings me back to elementary/middle school.
I think pink and yellow square make things more complicated, I think you can get C2 with the big area which is (a+b)(a+b) and substract it with the area of 4 triangle (4x1/2ab) hence (a+b)(a+b)-(2ab) = c2 and then simplified it to a2+2ab+b2-2ab = c2 then you can just substract 2ab and 2ab so it leave a2+b2=c2
I love how he took the time to break it down to show the proof is not a load of tosh. Far better than when I was in school and the teacher just drawing the a² + b² = c² in the board and using a metre stick to draw the “famous” ones towards the end. I wish I had more teachers like him. And through RUclips I can. I don’t need to be a child with time machine. You always learn and today I learnt more in these eleven minutes than that forty odd minute class, those 𝑥 years ago!
4:29 area of bigger square is (a+b)^2
And inner one is c^2 so the leftover, area of four triangles must be (a+b)^2-c^2.....
And we know area of those triangles is 4 times ab/2.
So(a^2 + b^2 +2ab) - c ^2= 4(ab/2)
a^2 + b^2 - c^2=2ab-2ab=0
a^2 + b^2 =c^2
Really admire his passion in teaching ....
I honestly can't wait to watch the rest of this channel's videos.Both well done and the enthusiasm made me smile.
Apparently 1.2K people are still smoking outside shop class though.
I don't know why but watching this makes me a bit emotional! I wish someone taught me PT this way 20 years ago when I was at school. I was terrible at Maths Methods and I don't think I ever fully grasped even the basics of PT. This video has helped me understand the fundamentals in 11 mins.
This is the best way to teach Pythagoras to kids. I would suggest two better ways to show left over squares a^2 and b^2 from 5:45:
a. Use like what Euclid did. The green triangles slide to the opposite sides.
b. to convince students that the first big square with a hole in the middle is the same with the latest square after moving/rotating two of the green triangles, that in 5:53 the bottom left triangle should be rotated to the right (pivot in the same contact point), instead of, like what you did, rotating the bottom right to the left. Then give two dot signs on the corner top left and right bottom to show that the same imaginary square is still intact. So, no need to move the new green rectangle at the bottom to the right and to convince the students about it that the new side lengths are the same, b+a and a+b.
I wish you were my math teacher back in the days! You make math entertaining! :)