Well, yes for schools that are specialized around the subject thus contain only people interested in it. But for people that are not interested in it it's not very comfortable. I always loved math lessons because they were taken like this but always understood that people that are not interested in math would prefer just hearing "It's pi r squared, learn that for the exam". And that's perfectly understandable. For example me, I am not interested in, I don't know... politics, for the instance, or economics. And when someone is trying to explain to me how companies internaly work or something like that I am like: "I just see what they do, how they do it and that's how I treat them." And for me, there's nothing more to it and I don't want it to be. It would be hypocrytic to treat fields I am personaly interested in differently than fields I am personaly not.
Took 11th grade trig, barely scraped by. Upon taking physics 3 years later I tried to teach it to myself. Turns out it's easy as hell, Nobody bothered to teach me why though.
He just explained the fundamental definition of integration. Edit:Watched this comment after 2 years. I see some good discussion below in the replies. Thank you everyone.
fun ...yeah, that’s the cool and challenging thing about what he was doing. Truth is that calculus could be taught at lower levels in this fashion. It opens the door to a variety of new perspectives on making math less of a drudgery at lower levels. That’s not math. That’s memorization.
@@Kandralla It's not really about what you would rather do but what works. Times tables are your foundation. If you become an adult without being able to do times tables as second nature you are quite impaired. It is used all the time. There should be a lot of repetition in learning like in times tables and bonds and other concepts but also a lot of more creative learning. There should be a balance. One should not be sacrificed to make it fun and then leave people with serious gaps in their functioning as adults. You need times tables for something basic like going shopping. It should be second nature and that is why there is repetition involved.
I’m 43 years old and have always been “good” at math,..... but I have never had anyone explain math to me the way you do. I wish I had teachers like you in high school!!! Great job! I love watching your channel. It will help me explain math to my child. Thanks 🙏🏽
That, and the fact that not many teachers just aren't enthusiastic about the profession. Many start out that way but due to lack of support, administration politics, disinterested students, etc., the passion they may have started out with just gets crushed. And, just like any other profession, after about 7 years, they burn out. Human nature. "Those that can, do. Those that can't, teach. Those that can't teach, teach 'gym'."
They don't have the time. He took 7 minutes to teach one basic formula. Take that long with every formula they need to know and you'd be there for years.
The problem with doing this in the classroom is how many varied students are in the room. To understand this explanation, you already have a working understanding of area and circumference and this lesson just cements that to a deeper level. If you don't have that understanding, this lesson is confusing and brings in many different concepts and drawings. Imagine a student asking "where did those rectangles come from?" or "do we have to know this for the test?" and how you answer that. This is a great video and is a great approach for tutoring or after class help. But it's a big risk in a classroom.
@@Ryvaken the first question feels like...inference? issues. the second question is a problem with the system itself, not a learning issue. if your school has always been "memorize this for a test" than youd be adverse to things that won't be on said test, but you still to know them.
I am 24, finished school, got an MEng and work as an engineer. I have only just properly understood why A=pi*r^2 now thanks to your video. If only more educators were like you.
@@17martinl integration might spit out the correct formula, but a purely visual explanation like this video can help one truly “get it”. Lots of people are really good at applying known formulas and techniques to get the result, without necessarily knowing the geometric or visual equivalent of what is happening in the intermediate steps.
Amazing lesson! Due to getting a degree in engineering many years ago, I had tons of math, and some very good instructors, but NOBODY ever explained the formulas of a circle like this! Excellent video! I love the fact that you don't just throw the formulas out there and expect people to remember them, but instead, in a very intuitive way, show HOW the formulas came about!
Same. My teacher never explained the whys. Our education system is designed to make students get higher grades, not bring out geniuses. Look at my people, they're more interested in politicizing everything.
@@bobfake3831 Is it though? Grades are based on your results on tests, presentations, exams etc., but every student can have a bad day - even those with a great understanding of a topic. Of course grades give a pointer on what level you're on, but they don't portray the full picture.
I have never met a teacher who didn't rejoice his ass off over a student who wanted to get deeper into the math. But be honest about how many students you have seen in school who would have wanted that. Unfortunately you stop going out of your way to demonstrate deeper layers of the math, after looking at students who don't give a crap about anything math related beyond just passing well enough to be left alone about it afterwards for 30 years.
But this isn't a proof, though. It's only showing why the formula makes sense. At that level of math class, teachers fail because they're not enthusiastic.
@@harrismazari5484 Are teachers in third world countries not rejoicing when students want to know more about the math they are teaching? I cannot say much about this context, but I guess it would make some kind of sense, since the math teachers there are probably worse paid and not as highly educated themselves. Its hard to become passionate about something in that case.
I think this guy teaches higher level or higher achieving classes. I got kids in my class in high school that don't know a length is CM and an area is CM^2. Would have lost them at the start already. lol.
S: Why should we pass the exam? T: It will help you be accepted into further education. S: Why should we be accepted into further education? T: It will help you get a job. S: Why should we get a job? T: To earn money. S: Why should we earn money? T: To buy things you need to survive. S: Why should we survive? T: Stop asking questions. S: Why should I stop asking questions? T: Because it is distracting you and the rest of the class from studying what you need to pass the exam.
You’re unlucky (or I’m lucky.) That’s not how my teachers (that I can remember) have ever acted with math. Okay, the curriculum itself doesn’t give the teachers a whole lot of room to really explain much. The goal of the system is to be efficient on time and so we usually gloss over the notes and practice worksheets and such to prepare for the test.
I am so glad I stumbled upon these videos Eddie! Looooooong ago I majored in math and minored in Chem and physics but never worked in those fields (worked in therapeutic recreation early on and a business manager in an elementary school later). These videos along with my old college books help me rekindle my love for math so much so that I am reading up on and teaching myself orbital mechanics. Thanks!
Hi Mr Woo, just thought I might share an interesting idea. So if you draw infinitely many concentric circles inside the original circle, you are going to essentially cover the entire area of the circle. Hence, the area of the original circle is just the sum of the areas of all the infinitely thin concentric circle ‘rings’. These rings will have radius r such that 0
As a student who is now studying calculus 2 in university, seeing these videos of simple concepts explained in such an interesting way makes me interested in math again. My high school teachers just didn’t quite have this level of understanding and didn’t make it nearly as interesting. Watching your videos makes me feel like I’m re-learning the fundamentals of math and I love it
Then you haven't seen a freehand circle by Al Overwich. (sp?). Math teacher in Ottawa Canada. One of his students posted a video of him drawing a circle.
You are such an amazing teacher. This is the third or 4th video I’ve watched and in every one you explain something I learned in school and have known for 20 years, but I member knew WHY. Teachers just gave us formulas, but never showed where those formulas come from.
Holy shit I got spooked out here. I sneezed in the beginning of the video and when he said bless you my jaw just dropped. It was perfectly timed with the sneeze in the video.
I had a great maths teacher when I was in high school. It made a huge difference in my life on so many levels. I'm no mathematician, but I love it still some 30 years later. And I try to be as inspiring as him when teaching at university. It's different. Kids are far more impressionable, but still, that's all thanks to him. I am quite sure Eddie Woo will have a similar impact on many of his students, as my teacher had. His style of teaching really reminds me of my maths teacher too. The best part: my teacher was 62 when I attended his class. This style of teaching keeps your mind young, keeps you young. When he retired we couldn't believe it. Thank you Klaus Nick.
I graduated college already so I have no idea why I'm watching these videos, but I never knew the origins of these formulas even though I was amazing at math.
Yeah it's a thing you may or may not suddenly notice when you're studying calculus and you'll go DUUUUUUDE Like for example getting the volume of a circle is just integrating the same equation again
I was expecting some other kind of "visual" aid, but this just blew my mind! I have never, ever seen it presented this way. I will be sharing this with others. I'll probably find out that they were already exposed to this method, but that doesn't matter, because finally, I have been. Wow, Mr. Woo (7 years later!!), this is fantastic!
A very beautiful way of using the already well known concepts and visuals of basic Geometry, to work out the area, rather than resorting to the comparatively higher Calculus. In fact, this method could be a precursor to the approximation techniques leading upto Integral Calculus.
Wish I had this kind of explanations by teachers back in school. My school life would have been such a good time. Though we did have a teacher who made us cut cardboard discs and measure perimeter with a string. Only if all teachers approached subjects like this my overall experience at school could have be soooooo less miserable. Great respect for teachers like you.
Sir namaste🙇♀️(नमस्ते).... I am from India 🇮🇳 When I was searching maths teachers then I came to know about you....and I also saw your interview on TEDX .....After that I start following you because your teaching method is outstanding..... Which help me a lot to understand maths in a different way......At last THANK YOU SIR🤗🤗 Huge respect from India☺☺🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🙇♀️
24 years old, however many years of math I've taken, and finally a teacher says, "That's where pi comes from." Is it so hard for American teachers to say what the hell it means instead of just saying, "because that's what it is."
What? The video doesn't show where pi comes from. It uses pi as a given constant and a method of getting to the formula of the area if you already know he formula for the circumference. He doesn't explain where pi comes from. He just says that that the circumference is 2r×pi.
@@pattininja95 Pi is the ratio of the circumference to the diameter. Draw any size circle, measure around the edge, measure across the centre, then divide the first measurement by the second and you'll get pi.
this guy is a sick teacher, I was lucky to have one like him in high school. its so funny, I remember that I got literally 100% percent in the class in grade 11 with my good teacher, (every question right on every single weekly test), but my marks went down by a fair bit in grade 12 with the not so good teacher....and I don't think it was because the material was that much harder. I attribute the success mostly to how well the material was taught to me
I wish I had teachers like you at Math class. This really is a fantastic way of learning the complexity of and beauty o Math. Your vids are outstanding. What a great teacher you are.
Alternative proof: You can also cut an extremely thin triangle from the circle from the center. Area of that triangle =0.5*b*r (where r is the radius, b is the base of the triangle) Now, if we add up all such triangles, we will get the area of the circle. So we have, Area of circle = 0.5*r*(sum of the lengths of triangle bases) = 0.5*r*(2*pi*r) =pi*r²
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This teacher could have saved me years of struggling with the why of math. I was just replicating the formulas without understanding the why (even throughout engineering in University 25 years). In 5 minutes he made me understand. Thus teacher will have so much impact on these kids.
It came to my mind, that it maybe would be nessecary to mention, that (and why) the slices form indeed a triangle and not another kind of shape. It's kind of trivial, but at the same time not self-explanatory, I think. But nice way to show the whole thing.
I'm a teacher at a vocational school in Germany and came across your videos while googling for an easily understandable way of explaining the Pythagorean Theorem. For my group it will just be a review but I'll use the proof you presented anyways. I really like your style of teaching. Engaging, interesting, easy to follow. Your fascination for maths comes across really well.
oh my god you have just made everything make sense for me, i always wondered why things worked in maths but it was never properly explained to me, thank you so much!!
I always remember the circumstance of a circle is the anti derivative of the area but I never asked or wondered where the formula came from because I never need it to know for school. Thank you for explaining it in such an easy way to understand. Love your videos.
Bravo, Monsieur! You have obviously done some differential calculus to get this idea. But it is fantastic to bring the principle in a geometry course. It does shed light on the mechanics of the thing. Well done!
How do you remember which one's which? *PI R SQUARED SOUNDS LIKE AREA TO ME, WHEN I NEED THE CIRCUMFERENCE I JUST USE PI D* My teacher singing this in class is the best thing ever. I'll never ever forget it.
We understand very easily Thankyou sir. I am Karthikeyan from kollihills Tamilnadu, India. I saw only 3 vedio (0! and divide by 0). Now I wish to see all of your lessons. Once again thankyou very much.
All he did was show how to take an integral of a linear function without calculus. Linear functions are always triangles, which is why they come out to be quadratic functions after integration. Very impressive to explain in terms of basic algebra though.
@@tc1817 I don't know about you, but when in school, many kids don't know what to ask. It helps if teachers teach. Maybe you were a more perfect kid? haha
@@TheZombiecowmeat I'm just saying that if you wanted to know where pi comes from, you could ask. I'm 1000% sure that your math teachers at some point explained the relationships between r, d, c and pi. It never occurred to you to think "why is it 3.14...." and not some other number?
So what's your point? You could also find the area by cutting a circle out of a piece of metal, melting the metal and pouring the melt into a square mold of known dimensions, then measuring the thickness and then multiplying the area of the mold by the thickness and taking the square root of the result. However, when you're teaching seventh graders you start with the basics.
Just taking me to my school days. I had some great teachers but this guy has some passion for teaching because nobody teaches you how formulas are derived
This method of teaching - not just the what, but the why and the how - is the best method of teaching
Well, yes for schools that are specialized around the subject thus contain only people interested in it. But for people that are not interested in it it's not very comfortable. I always loved math lessons because they were taken like this but always understood that people that are not interested in math would prefer just hearing "It's pi r squared, learn that for the exam". And that's perfectly understandable. For example me, I am not interested in, I don't know... politics, for the instance, or economics. And when someone is trying to explain to me how companies internaly work or something like that I am like: "I just see what they do, how they do it and that's how I treat them." And for me, there's nothing more to it and I don't want it to be. It would be hypocrytic to treat fields I am personaly interested in differently than fields I am personaly not.
@@Alialun2 I think everyone should learn the lessons like this in the schools, everyone needs the learn fundamentals of every lesson.
on which level though? note that circumference and area are taught on level 4 elementary schools.
it's because he's asian
Took 11th grade trig, barely scraped by. Upon taking physics 3 years later I tried to teach it to myself. Turns out it's easy as hell, Nobody bothered to teach me why though.
He just explained the fundamental definition of integration.
Edit:Watched this comment after 2 years. I see some good discussion below in the replies. Thank you everyone.
LMAO I love it. His ability to explain to what I assume to be highschool level students is really sublime
fun ...yeah, that’s the cool and challenging thing about what he was doing. Truth is that calculus could be taught at lower levels in this fashion. It opens the door to a variety of new perspectives on making math less of a drudgery at lower levels. That’s not math. That’s memorization.
Reiiiiiimmmannnn sum
@@Kandralla It's not really about what you would rather do but what works. Times tables are your foundation. If you become an adult without being able to do times tables as second nature you are quite impaired. It is used all the time. There should be a lot of repetition in learning like in times tables and bonds and other concepts but also a lot of more creative learning. There should be a balance. One should not be sacrificed to make it fun and then leave people with serious gaps in their functioning as adults. You need times tables for something basic like going shopping. It should be second nature and that is why there is repetition involved.
One of the biggest mind blown moments was when I realized than the circumference was just the derivative of the area.
This is how the overall society benefits when individuals follow their passion and love what they do. Excellent presentation 👍👌
"That's a sneeze and a half"
Lmao
sneeze²
Maybe he was the infamous teacher MatPat had.
@@erikbjork8220 1.5sneeze
@@pawpatrol55 1.5×10¹=15
@@pawpatrol55 On my computer simply AltGr+1, you could also try first ^ and then 1. And if that doesn't help, Google is your friend.
Wow! Your teaching makes me want to be a circle
WHO FOUND PI?
In a way, we are all billions, if not trillions of tiny 3D circles
@@rupamjyotigogoi6138 WA Warehouse
4/9/2020
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@@Hyblup umm i believe a 3d circle is called a sphere if I’m not mistaken? 😆
It makes me want pizza, or pie.
You have a gift for teaching and communicating! Well done!
I’m 43 years old and have always been “good” at math,..... but I have never had anyone explain math to me the way you do. I wish I had teachers like you in high school!!! Great job! I love watching your channel. It will help me explain math to my child.
Thanks 🙏🏽
The reason that more teachers aren't this good is that they don't understand the material.
That, and the fact that not many teachers just aren't enthusiastic about the profession.
Many start out that way but due to lack of support, administration politics, disinterested students, etc., the passion they may have started out with just gets crushed.
And, just like any other profession, after about 7 years, they burn out. Human nature.
"Those that can, do.
Those that can't, teach.
Those that can't teach,
teach 'gym'."
They understand their material, but think of a teacher's life like put your life in your teacher's shoes
What an embarrassingly ignorant comment.
The only thing harder to find than a good teacher is a good student. Just saying ; )
They don't have the time. He took 7 minutes to teach one basic formula. Take that long with every formula they need to know and you'd be there for years.
Is anyone else just watching these for fun
I just graduated with a B.S in Mathematics and I still find myself watching this guy’s videos.
@@movieguy117 beep boop
I totally have nothing to do with maths, just used to study it. And I still end up watching his awesome lessons.
Me I was terrible at maths.. Now relearning it for fun
Yes... And I am not even a student. A middle-aged medical doctor!
Never seen an explanation ever like he just did. Jaw dropping. He made me wish I had a teacher like him back in High School.
The problem with doing this in the classroom is how many varied students are in the room. To understand this explanation, you already have a working understanding of area and circumference and this lesson just cements that to a deeper level. If you don't have that understanding, this lesson is confusing and brings in many different concepts and drawings. Imagine a student asking "where did those rectangles come from?" or "do we have to know this for the test?" and how you answer that.
This is a great video and is a great approach for tutoring or after class help. But it's a big risk in a classroom.
@@Ryvaken the first question feels like...inference? issues. the second question is a problem with the system itself, not a learning issue.
if your school has always been "memorize this for a test" than youd be adverse to things that won't be on said test, but you still to know them.
I am 24, finished school, got an MEng and work as an engineer. I have only just properly understood why A=pi*r^2 now thanks to your video. If only more educators were like you.
you never had to integrate a circle?
@@17martinl integration might spit out the correct formula, but a purely visual explanation like this video can help one truly “get it”. Lots of people are really good at applying known formulas and techniques to get the result, without necessarily knowing the geometric or visual equivalent of what is happening in the intermediate steps.
The explanation in the video literally is integration. In fact this is one of the best illustrations of integration!
@@samsowden The idea behind the infinite number of strips is essentially a Riemann Sum, if I recall correctly.
@@elmarko9051 ye, a riemann sum
Amazing lesson! Due to getting a degree in engineering many years ago, I had tons of math, and some very good instructors, but NOBODY ever explained the formulas of a circle like this! Excellent video! I love the fact that you don't just throw the formulas out there and expect people to remember them, but instead, in a very intuitive way, show HOW the formulas came about!
*draws near perfect circle* “I could draw better”
Asians, man.
@@Birrrrra Ofcourse you had to make it a race thing. smh
@@missionpupa chill dude, that was a dad joke, and apparently went over your head
@@allat0nce dad joke my ass.
@@missionpupa It's a joke based on the generalization of asians being superb at everything. Not a bad joke even
This is a good precursor to calc. I wish my math teacher described things this way.
Indeed, my math teacher was talking about those "pizza-slices" but I didn't get the point. Luckily I got it now👍🏼
Ryan Ford Has
Same. My teacher never explained the whys. Our education system is designed to make students get higher grades, not bring out geniuses. Look at my people, they're more interested in politicizing everything.
Unluckily for you, grades actually are a decent indicator for understanding of a topic.
@@bobfake3831 Is it though? Grades are based on your results on tests, presentations, exams etc., but every student can have a bad day - even those with a great understanding of a topic. Of course grades give a pointer on what level you're on, but they don't portray the full picture.
Our teacher in school: Just remember the formula dont ask why its like that.
Exactly, critical thinkers not allowed!
I have never met a teacher who didn't rejoice his ass off over a student who wanted to get deeper into the math.
But be honest about how many students you have seen in school who would have wanted that.
Unfortunately you stop going out of your way to demonstrate deeper layers of the math, after looking at students who don't give a crap about anything math related beyond just passing well enough to be left alone about it afterwards for 30 years.
@@AliothAncalagon that's because you didn't go to suchool in India or any other third world country
But this isn't a proof, though. It's only showing why the formula makes sense. At that level of math class, teachers fail because they're not enthusiastic.
@@harrismazari5484 Are teachers in third world countries not rejoicing when students want to know more about the math they are teaching?
I cannot say much about this context, but I guess it would make some kind of sense, since the math teachers there are probably worse paid and not as highly educated themselves. Its hard to become passionate about something in that case.
2:00 Drawing a circle freehand so good like that just further proves Eddie is a magician!!
Watching this makes me wanna become a maths teacher when I'm older.
Josh Doyle “maths” first you should probably graduate English.
Darth Maul "maths" first you should probably graduate Brit or Aussie English.
Darth Maul Maybe you should move out of America for a day. Maths is acceptable
@@iamadragonborn mathematics
I think this guy teaches higher level or higher achieving classes. I got kids in my class in high school that don't know a length is CM and an area is CM^2. Would have lost them at the start already. lol.
Me: Why?
Teacher: It will help you pass the exam.
S: Why should we pass the exam?
T: It will help you be accepted into further education.
S: Why should we be accepted into further education?
T: It will help you get a job.
S: Why should we get a job?
T: To earn money.
S: Why should we earn money?
T: To buy things you need to survive.
S: Why should we survive?
T: Stop asking questions.
S: Why should I stop asking questions?
T: Because it is distracting you and the rest of the class from studying what you need to pass the exam.
You’re unlucky (or I’m lucky.)
That’s not how my teachers (that I can remember) have ever acted with math. Okay, the curriculum itself doesn’t give the teachers a whole lot of room to really explain much. The goal of the system is to be efficient on time and so we usually gloss over the notes and practice worksheets and such to prepare for the test.
@@Zalamandar you're forgetting "how?"
I am so glad I stumbled upon these videos Eddie! Looooooong ago I majored in math and minored in Chem and physics but never worked in those fields (worked in therapeutic recreation early on and a business manager in an elementary school later). These videos along with my old college books help me rekindle my love for math so much so that I am reading up on and teaching myself orbital mechanics. Thanks!
Eddie, this and your other videos are WONDERFUL !!! THANK YOU !
Hi Mr Woo, just thought I might share an interesting idea.
So if you draw infinitely many concentric circles inside the original circle, you are going to essentially cover the entire area of the circle.
Hence, the area of the original circle is just the sum of the areas of all the infinitely thin concentric circle ‘rings’. These rings will have radius r such that 0
***** Yeah! I'm going to watch those two videos now
Even I thought the same ! , Even if we differciate area of circle with respect to R we will get circumference of the circle
Woah cool
Wasn't video explanation the same in principle?
Durrr
As a student who is now studying calculus 2 in university, seeing these videos of simple concepts explained in such an interesting way makes me interested in math again. My high school teachers just didn’t quite have this level of understanding and didn’t make it nearly as interesting. Watching your videos makes me feel like I’m re-learning the fundamentals of math and I love it
That was the best handmade circle I've ever seen
Then you haven't seen a freehand circle by Al Overwich. (sp?). Math teacher in Ottawa Canada. One of his students posted a video of him drawing a circle.
ua-cam.com/video/W7CE8f3Z630/v-deo.html
@@eugene188 WHO FOUND 🥧
@@stevethea5250 what??
@@jacinth8993 who founded pi
I searched for explanations about the area of the circle and this one is the best and most clear explanation I've ever found!! Amazing teacher!!!
Jose A. Alpízar C. The Pizza slicing is - to my opinion - even more intuitive.
This man’s method of teaching is my model for tutoring people. Dear lord, does he make it all so connected
The world is a better place with ppl like you in it. Thanks for improving our understanding of these things that we never learn.
As soon as he pointed out it becomes a triangle it all just clicked. So well explained
This uses the idea of calculus without resorting to the math. Amazing stuffs.
Best teacher ever!!!
You make the hardest things so easy to understand!
You are such an amazing teacher. This is the third or 4th video I’ve watched and in every one you explain something I learned in school and have known for 20 years, but I member knew WHY. Teachers just gave us formulas, but never showed where those formulas come from.
Holy shit I got spooked out here. I sneezed in the beginning of the video and when he said bless you my jaw just dropped. It was perfectly timed with the sneeze in the video.
I had a great maths teacher when I was in high school. It made a huge difference in my life on so many levels. I'm no mathematician, but I love it still some 30 years later. And I try to be as inspiring as him when teaching at university. It's different. Kids are far more impressionable, but still, that's all thanks to him. I am quite sure Eddie Woo will have a similar impact on many of his students, as my teacher had. His style of teaching really reminds me of my maths teacher too. The best part: my teacher was 62 when I attended his class. This style of teaching keeps your mind young, keeps you young. When he retired we couldn't believe it. Thank you Klaus Nick.
I graduated college already so I have no idea why I'm watching these videos, but I never knew the origins of these formulas even though I was amazing at math.
Vincent Y. This goes into calculus since the length of each concentric circle is dx. It’s honestly very satisfying if you ask me.
Then you’re not really amazing at math
you can be good at math and also try to derive formulas yourself, just for curiosity
Yeah it's a thing you may or may not suddenly notice when you're studying calculus and you'll go DUUUUUUDE
Like for example getting the volume of a circle is just integrating the same equation again
@@guythat779 what exactly is the volume of a circle ...?
More teacher like you need in our country the way of explanation is more clear than package bottle 🍼🍼🍼🍼🍼🍼
Eddie: “what unit would you use to describe this circle?”
Me, an American: “Inches”
Student: “Centimeters”
Me: “eh, that system is better anyway”
Imperial measurements is not standardized due to an inch, a foot etc can vary. But the metric is standardized.
Treason
Me, who loves the metric system: DECIMETERS!
(that's 10 cm, in between cm and m, which is for this scale)
No, i do not run 300 mm pipe. I run 12"pipe.
@@andmos1001 Imperial units are defined by metric terms, so they don't change.
I am in calc 3 and I am still amazed at what I am learning from videos like these. Keep on going.
Sneezes in 2018: giggle giggle bless you
Sneezes in 2020: SHUT THIS PLACE DOWN NOW!!
Was thinking the same 😂😂😂
If she sneezed in class today she'd be SWAT teamed!
Jepp 😷
I just wished all teachers did what you are doing.. hats off to you for the details and solid fundamentals you are instilling to the kids..
0:17 ahhhh the good ol pre covid time...
I mean, sneezes aren't really a covid symptom 🤷♂️
@@pattsw but it is a method of transmission from person to person for covid which is a worry.
I was expecting some other kind of "visual" aid, but this just blew my mind! I have never, ever seen it presented this way. I will be sharing this with others. I'll probably find out that they were already exposed to this method, but that doesn't matter, because finally, I have been.
Wow, Mr. Woo (7 years later!!), this is fantastic!
A very beautiful way of using the already well known concepts and visuals of basic Geometry, to work out the area, rather than resorting to the comparatively higher Calculus.
In fact, this method could be a precursor to the approximation techniques leading upto Integral Calculus.
3 years after this one has come up, many years since I was in uni and well, someone explains so I can understand. Thank you Mr Woo
why are you watching it now?
2:00 he draws a perfect circle 😲
not perfect... however pretty good for a hand drawn circle by freehand. However not the best hand drawn circle.
Pi of his circle isn't 3.14 sure😂
"Eeeeh, I've done better."
3:32 start drawing perfect potatoes...
@blayral JAJAJAAJA
Wish I had this kind of explanations by teachers back in school. My school life would have been such a good time.
Though we did have a teacher who made us cut cardboard discs and measure perimeter with a string. Only if all teachers approached subjects like this my overall experience at school could have be soooooo less miserable. Great respect for teachers like you.
Sir namaste🙇♀️(नमस्ते)....
I am from India 🇮🇳
When I was searching maths teachers then I came to know about you....and I also saw your interview on TEDX .....After that I start following you because your teaching method is outstanding.....
Which help me a lot to understand maths in a different way......At last THANK YOU SIR🤗🤗
Huge respect from India☺☺🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🙇♀️
He is so awesome man... His way of teaching is lobb😍
24 years old, however many years of math I've taken, and finally a teacher says, "That's where pi comes from." Is it so hard for American teachers to say what the hell it means instead of just saying, "because that's what it is."
What? The video doesn't show where pi comes from. It uses pi as a given constant and a method of getting to the formula of the area if you already know he formula for the circumference.
He doesn't explain where pi comes from. He just says that that the circumference is 2r×pi.
@@borstenpinsel Then I want to ask you this. Why is pi 3.14159.... Where do we get the number from
@@pattininja95 Pi is the ratio of the circumference to the diameter. Draw any size circle, measure around the edge, measure across the centre, then divide the first measurement by the second and you'll get pi.
@@j5300 which is exactly what he says in this video, hence my comment
borstenpinsel the teacher mentions that pi is the ratio between the circumference and diameter of a circle. He explains where it comes from
I don’t watch you videos religiously enough to give you a sub, but your such a good fucking teacher that you earned it for me. Keep up the good work!
Ha, for a second I thought, "Ohhh, here we go, here comes the calculus!"
a beautiful way of teaching integration without naming it ! Bravo !
this guy is a sick teacher, I was lucky to have one like him in high school. its so funny, I remember that I got literally 100% percent in the class in grade 11 with my good teacher, (every question right on every single weekly test), but my marks went down by a fair bit in grade 12 with the not so good teacher....and I don't think it was because the material was that much harder. I attribute the success mostly to how well the material was taught to me
Yep, the difference in teaching quality can EQUATE (haha) to a similar difference in learning quality.
I wish I had teachers like you at Math class. This really is a fantastic way of learning the complexity of and beauty o Math.
Your vids are outstanding. What a great teacher you are.
When I was in school, I was just given an equation
Oh wow. No idea how I ended up here, not even doing anything Mathy, but such a beautiful explanation of something I learnt by heart 30 years ago.
Alternative proof:
You can also cut an extremely thin triangle from the circle from the center.
Area of that triangle =0.5*b*r
(where r is the radius, b is the base of the triangle)
Now, if we add up all such triangles, we will get the area of the circle. So we have,
Area of circle = 0.5*r*(sum of the lengths of triangle bases)
= 0.5*r*(2*pi*r)
=pi*r²
He says that at 3:20
The universe need teachers like u for a true change...
This was from the bottom of my heart. Love u sir ❤
00:17 gosh that sneezed scared the hell out of me!
Awesome 👏🏻, he just explained the area of circle and integration in so beautiful way. 🙏🙏🙏
0:16 Thought someone stepped on a dogs paw or something wtf.
GZA 🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣
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🤣🤣🤣
This teacher could have saved me years of struggling with the why of math. I was just replicating the formulas without understanding the why (even throughout engineering in University 25 years). In 5 minutes he made me understand. Thus teacher will have so much impact on these kids.
It came to my mind, that it maybe would be nessecary to mention, that (and why) the slices form indeed a triangle and not another kind of shape. It's kind of trivial, but at the same time not self-explanatory, I think.
But nice way to show the whole thing.
I'm a teacher at a vocational school in Germany and came across your videos while googling for an easily understandable way of explaining the Pythagorean Theorem. For my group it will just be a review but I'll use the proof you presented anyways. I really like your style of teaching. Engaging, interesting, easy to follow. Your fascination for maths comes across really well.
This is why geometry is so important, formulas in algebra all have reasons behind them
Man his method of teaching is outstanding.
I never literally understood the area of circle but after this video my all concepts are clear
Thanks Sir
I just realized...
*THE CIRCUMFERENCE OF A CIRCLE IS THE DIFFERENTIATION OF ITS AREA WITH RESPECT TO R.*
its not exactly a gradient...
oh my god you have just made everything make sense for me, i always wondered why things worked in maths but it was never properly explained to me, thank you so much!!
This guy has both knowledge and understanding, unlike most teachers who only have knowledge
I always remember the circumstance of a circle is the anti derivative of the area but I never asked or wondered where the formula came from because I never need it to know for school. Thank you for explaining it in such an easy way to understand. Love your videos.
We definitely need more Asian math teachers in our schools. That's a compliment.
The best explanation of this I have ever heard. I wish you had been my math teacher at school 👍
decimeters. underrated unit of measurement. fun fact: 1 cubic decimeter = 1 litre
Bravo, Monsieur! You have obviously done some differential calculus to get this idea. But it is fantastic to bring the principle in a geometry course. It does shed light on the mechanics of the thing. Well done!
dat sneeze holy shit
A sneeze and a half*
Sneeze^2
(Sneeze)^2+-(Sneeze)^2
Solve for S.
Got a kid in school learning this stuff. Excellent refresher so I can help him when he asks. Thank you.
Watching this while knowing integration and only connecting at the beginning that PIxr^2 is the integral of 2PIr
Very few people has ability to explain mathematics in simple and interesting way. We need teachers like him.🙏🙏
00:20 Weird to think that that sneeze would've been a much bigger deal had it happened these days
I never commented.. before but ur way of teaching made me do that.......u r awesome sir
How do you remember which one's which?
*PI R SQUARED SOUNDS LIKE AREA TO ME, WHEN I NEED THE CIRCUMFERENCE I JUST USE PI D*
My teacher singing this in class is the best thing ever. I'll never ever forget it.
*when I need the circumference
@@suhailmall98 my bad, fixed it
I REMEMBER THIS
Apple pies are square (A= pi X r^2)... cherry pie delight (C= pi X d ) is how I was taught it 😂😂
That was awesome. Never seen that proof and it is wonderfully elegant. Also props Eddie - that first circle you drew was amazing for freehand!
Dead classroom, I verbally said “wow” when he finished the proof. Where’s the enthusiasm lmao
We understand very easily Thankyou sir.
I am Karthikeyan from kollihills Tamilnadu, India. I saw only 3 vedio (0! and divide by 0).
Now I wish to see all of your lessons.
Once again thankyou very much.
tbh that circle may actually be close to 2m, but just may not look like it
This was probably one of the coolest explanations I’ve ever seen.
Teaching my kids area tomorrow and I will definitely be using this
You didnt explain why putting slices between each other draws a straight line and not an exponential line growth
because circumference is directly proportional to radius
We can proof it simply by finite element method. It is concept in calculus
All he did was show how to take an integral of a linear function without calculus. Linear functions are always triangles, which is why they come out to be quadratic functions after integration. Very impressive to explain in terms of basic algebra though.
What's so impressive about it? This is the basics of greek geometry.
Yes , don’t worry, we think you’re clever too. However he did it with clarity and kept the kids engaged , and that’s the actual clever bit.
You, Sir, are a really good teacher!
I've been through endless amounts of math classes in my lifetime, and never has anyone every told me the WHY.
You're full of shit. Any high school math teacher can tell you where pi comes from. What exactly were your questions?
@@tc1817 "can" tell you, sure. "Did" tell us, no.
@@TheZombiecowmeat You didn't ask.
@@tc1817 I don't know about you, but when in school, many kids don't know what to ask. It helps if teachers teach. Maybe you were a more perfect kid? haha
@@TheZombiecowmeat I'm just saying that if you wanted to know where pi comes from, you could ask. I'm 1000% sure that your math teachers at some point explained the relationships between r, d, c and pi. It never occurred to you to think "why is it 3.14...." and not some other number?
this made me rethink about the whole education system in my country!
you are such a nice teacher eddie!
Love from NEPAL
Everyone is talking about the nicely drawn circle, but I'm here exstatic he's introducing the metric system to the english speaking world.
Australia is metric
This sparks joy. Thanks
When you realize you never gonna slice a perfect 6 pizza pieces because pi ruined it.
Fullus Retardus But you'll never get a perfect pizza in the first place because of the same reason.
He Who Judges oh shit
Of course you can a pizza with (Pi*r²)/6 area of slice of every pizza piece
The good thing is, it is made of atoms. Yes people, finite, rational and beautiful (just don't bring the quantum mechanics guys) ;)
You'll get 6.283 slices I'd wager.
This is a great abstraction of integration in polar coordinates
Did you just show a visualization of differentiation? When you differentiate area you get circumference..
He is so perfect in his explanations Everyone wants a teacher like him. Respect you Sir.Those students are so lucky
Imagine being so bored out of your mind you click this video and read my comment.
Ya got me, an ADHD patient
And I've never seen a proof more elegant than this
Hey Eddie! We can also find the area of circle by integrating the circumfernce of that circle.
So what's your point? You could also find the area by cutting a circle out of a piece of metal, melting the metal and pouring the melt into a square mold of known dimensions, then measuring the thickness and then multiplying the area of the mold by the thickness and taking the square root of the result. However, when you're teaching seventh graders you start with the basics.
@@dhy5342 no you actually cant. You messed up slightly on your calculations.
Just taking me to my school days. I had some great teachers but this guy has some passion for teaching because nobody teaches you how formulas are derived