This method of teaching - not just the what, but the why and the how - is the best method of teaching
@Alialun24 жыл бұрын
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.
@Uykusuz934 жыл бұрын
@@Alialun2 I think everyone should learn the lessons like this in the schools, everyone needs the learn fundamentals of every lesson.
@adam-nf1ig4 жыл бұрын
on which level though? note that circumference and area are taught on level 4 elementary schools.
@proletariatpashka19564 жыл бұрын
it's because he's asian
@mellinghedd2674 жыл бұрын
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.
@tarunbanala76335 жыл бұрын
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.
@ajbarsanti4 жыл бұрын
LMAO I love it. His ability to explain to what I assume to be highschool level students is really sublime
@edwardbraunhut51204 жыл бұрын
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.
@wizcombo4 жыл бұрын
Reiiiiiimmmannnn sum
@Martin-pb7ts4 жыл бұрын
@@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.
@logannance104 жыл бұрын
One of the biggest mind blown moments was when I realized than the circumference was just the derivative of the area.
@__Vijay__894 жыл бұрын
This is how the overall society benefits when individuals follow their passion and love what they do. Excellent presentation 👍👌
@MrBobTheLion5 жыл бұрын
Wow! Your teaching makes me want to be a circle
@stevethea52504 жыл бұрын
WHO FOUND PI?
@Hyblup4 жыл бұрын
In a way, we are all billions, if not trillions of tiny 3D circles
@stevethea52504 жыл бұрын
@@rupamjyotigogoi6138 WA Warehouse 4/9/2020 Notify me Vic Warehouse 8/9/2020
@The-ct1xq4 жыл бұрын
@@Hyblup umm i believe a 3d circle is called a sphere if I’m not mistaken? 😆
@aankwenti3 жыл бұрын
It makes me want pizza, or pie.
@bedoe96845 жыл бұрын
"That's a sneeze and a half" Lmao
@erikbjork82205 жыл бұрын
sneeze²
5 жыл бұрын
Maybe he was the infamous teacher MatPat had.
@Safwan.Hossain4 жыл бұрын
@@erikbjork8220 1.5sneeze
4 жыл бұрын
@@pawpatrol55 1.5×10¹=15
4 жыл бұрын
@@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.
@CopyrightCreators4 жыл бұрын
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 🙏🏽
@danieldraper44785 жыл бұрын
You have a gift for teaching and communicating! Well done!
@justinwu522610 жыл бұрын
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
@justinwu522610 жыл бұрын
***** Yeah! I'm going to watch those two videos now
@itssathyatalks39966 жыл бұрын
Even I thought the same ! , Even if we differciate area of circle with respect to R we will get circumference of the circle
@ShanRauf1246 жыл бұрын
Woah cool
@tempname82636 жыл бұрын
Wasn't video explanation the same in principle?
@crm12256 жыл бұрын
Durrr
@johnmackay77304 жыл бұрын
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.
@17martinl4 жыл бұрын
you never had to integrate a circle?
@ckannan904 жыл бұрын
@@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.
@samsowden3 жыл бұрын
The explanation in the video literally is integration. In fact this is one of the best illustrations of integration!
@elmarko90513 жыл бұрын
@@samsowden The idea behind the infinite number of strips is essentially a Riemann Sum, if I recall correctly.
@98danielray3 жыл бұрын
@@elmarko9051 ye, a riemann sum
@keesleo47854 жыл бұрын
Is anyone else just watching these for fun
@movieguy1174 жыл бұрын
I just graduated with a B.S in Mathematics and I still find myself watching this guy’s videos.
@jadedmarrow39404 жыл бұрын
@@movieguy117 beep boop
@platonshubin4 жыл бұрын
I totally have nothing to do with maths, just used to study it. And I still end up watching his awesome lessons.
@slappy_chimp4 жыл бұрын
Me I was terrible at maths.. Now relearning it for fun
@KartikAtre3 жыл бұрын
Yes... And I am not even a student. A middle-aged medical doctor!
@Alberturkey546 жыл бұрын
The reason that more teachers aren't this good is that they don't understand the material.
@burnerjack015 жыл бұрын
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'."
@moho96985 жыл бұрын
They understand their material, but think of a teacher's life like put your life in your teacher's shoes
@floydpinkerton79545 жыл бұрын
What an embarrassingly ignorant comment.
@brenttaylordotus5 жыл бұрын
The only thing harder to find than a good teacher is a good student. Just saying ; )
@smoog5 жыл бұрын
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.
@Drof11076 жыл бұрын
This is a good precursor to calc. I wish my math teacher described things this way.
@rickt1516 жыл бұрын
Indeed, my math teacher was talking about those "pizza-slices" but I didn't get the point. Luckily I got it now👍🏼
@garyfox18986 жыл бұрын
Ryan Ford Has
@aqimjulayhi87985 жыл бұрын
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.
@bobfake38315 жыл бұрын
Unluckily for you, grades actually are a decent indicator for understanding of a topic.
@waaahl5 жыл бұрын
@@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.
@Ollie0llie6 жыл бұрын
*draws near perfect circle* “I could draw better”
@Birrrrra4 жыл бұрын
Asians, man.
@missionpupa4 жыл бұрын
@@Birrrrra Ofcourse you had to make it a race thing. smh
@allat0nce4 жыл бұрын
@@missionpupa chill dude, that was a dad joke, and apparently went over your head
@missionpupa4 жыл бұрын
@@allat0nce dad joke my ass.
@NinjaCactus004 жыл бұрын
@@missionpupa It's a joke based on the generalization of asians being superb at everything. Not a bad joke even
@elguaporeyes20123 жыл бұрын
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.
@Ryvaken2 жыл бұрын
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.
@kaiseremotion8542 жыл бұрын
@@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.
@jszlauko Жыл бұрын
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!
@sirjoj16417 жыл бұрын
Watching this makes me wanna become a maths teacher when I'm older.
@darthmaul536 жыл бұрын
Josh Doyle “maths” first you should probably graduate English.
@beatsbydave326 жыл бұрын
Darth Maul "maths" first you should probably graduate Brit or Aussie English.
@cadden92406 жыл бұрын
Darth Maul Maybe you should move out of America for a day. Maths is acceptable
@AyushGupta-yj8jz6 жыл бұрын
@@iamadragonborn mathematics
@eugene1886 жыл бұрын
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.
@shashankdegloorkar4 жыл бұрын
Our teacher in school: Just remember the formula dont ask why its like that.
@JoseRodriguez-rx4ck4 жыл бұрын
Exactly, critical thinkers not allowed!
@AliothAncalagon4 жыл бұрын
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.
@harrismazari54844 жыл бұрын
@@AliothAncalagon that's because you didn't go to suchool in India or any other third world country
@znhait4 жыл бұрын
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.
@AliothAncalagon4 жыл бұрын
@@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.
@tirthajyotighosh6964 жыл бұрын
Me: Why? Teacher: It will help you pass the exam.
@Zalamandar3 жыл бұрын
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.
@georgesracingcar77013 жыл бұрын
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.
@olianims3 жыл бұрын
@@Zalamandar you're forgetting "how?"
@vincenty.89196 жыл бұрын
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.
@AngelRivera-mc8zc6 жыл бұрын
Vincent Y. This goes into calculus since the length of each concentric circle is dx. It’s honestly very satisfying if you ask me.
@pugboi80175 жыл бұрын
Then you’re not really amazing at math
@JorgetePanete5 жыл бұрын
you can be good at math and also try to derive formulas yourself, just for curiosity
@guythat7795 жыл бұрын
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
@chopun38624 жыл бұрын
@@guythat779 what exactly is the volume of a circle ...?
@nockynock48402 жыл бұрын
2:00 Drawing a circle freehand so good like that just further proves Eddie is a magician!!
@Towl356 жыл бұрын
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!
@BMGBOX Жыл бұрын
Eddie, this and your other videos are WONDERFUL !!! THANK YOU !
@ΝικοςΚαρακασης-β1υ6 жыл бұрын
That was the best handmade circle I've ever seen
@eugene1886 жыл бұрын
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.
@jacinth89936 жыл бұрын
kzbin.info/www/bejne/jWimdmucaL9paZI
@stevethea52504 жыл бұрын
@@eugene188 WHO FOUND 🥧
@eugene1884 жыл бұрын
@@stevethea5250 what??
@stevethea52504 жыл бұрын
@@jacinth8993 who founded pi
@the_picsopedia4 жыл бұрын
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
@jaireidca3 жыл бұрын
He says that at 3:20
@TechandStuff6 жыл бұрын
2:00 he draws a perfect circle 😲
@livedandletdie6 жыл бұрын
not perfect... however pretty good for a hand drawn circle by freehand. However not the best hand drawn circle.
@redfrommars53666 жыл бұрын
Pi of his circle isn't 3.14 sure😂
@kameronpeterson36016 жыл бұрын
"Eeeeh, I've done better."
@blayral6 жыл бұрын
3:32 start drawing perfect potatoes...
@ta_helado6 жыл бұрын
@blayral JAJAJAAJA
@joshpierce78204 жыл бұрын
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
@Terziak4 жыл бұрын
As soon as he pointed out it becomes a triangle it all just clicked. So well explained
@andersfejer73864 жыл бұрын
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.
@jc81534 жыл бұрын
This man’s method of teaching is my model for tutoring people. Dear lord, does he make it all so connected
@petercouchey3 жыл бұрын
Eddie: “what unit would you use to describe this circle?” Me, an American: “Inches” Student: “Centimeters” Me: “eh, that system is better anyway”
@andmos10013 жыл бұрын
Imperial measurements is not standardized due to an inch, a foot etc can vary. But the metric is standardized.
@jgod13413 жыл бұрын
Treason
@eliotlong51843 жыл бұрын
Me, who loves the metric system: DECIMETERS! (that's 10 cm, in between cm and m, which is for this scale)
@scotthix29263 жыл бұрын
No, i do not run 300 mm pipe. I run 12"pipe.
@ilcyclista13 жыл бұрын
@@andmos1001 Imperial units are defined by metric terms, so they don't change.
6 жыл бұрын
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!!!
@robertgumpi72356 жыл бұрын
Jose A. Alpízar C. The Pizza slicing is - to my opinion - even more intuitive.
@lorenzobelli41743 жыл бұрын
0:17 ahhhh the good ol pre covid time...
@pattsw3 жыл бұрын
I mean, sneezes aren't really a covid symptom 🤷♂️
@Sohlstyce3 жыл бұрын
@@pattsw but it is a method of transmission from person to person for covid which is a worry.
@pattininja954 жыл бұрын
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."
@borstenpinsel4 жыл бұрын
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.
@pattininja954 жыл бұрын
@@borstenpinsel Then I want to ask you this. Why is pi 3.14159.... Where do we get the number from
@j53004 жыл бұрын
@@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.
@pattininja954 жыл бұрын
@@j5300 which is exactly what he says in this video, hence my comment
@anawaz1894 жыл бұрын
borstenpinsel the teacher mentions that pi is the ratio between the circumference and diameter of a circle. He explains where it comes from
@karthikeyankrishnamoorthy19394 жыл бұрын
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.
@kev73554 жыл бұрын
This uses the idea of calculus without resorting to the math. Amazing stuffs.
@subterreanhighrise3 жыл бұрын
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.
@darknight36136 жыл бұрын
Best teacher ever!!! You make the hardest things so easy to understand!
@eepower5 жыл бұрын
The world is a better place with ppl like you in it. Thanks for improving our understanding of these things that we never learn.
@brian48043 жыл бұрын
Sneezes in 2018: giggle giggle bless you Sneezes in 2020: SHUT THIS PLACE DOWN NOW!!
@Sameer.K23 жыл бұрын
Was thinking the same 😂😂😂
@NotMarkKnopfler3 жыл бұрын
If she sneezed in class today she'd be SWAT teamed!
@larss3373 жыл бұрын
Jepp 😷
@thomasliptrott38344 жыл бұрын
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.
@ritatiwari88434 жыл бұрын
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☺☺🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🙇♀️
@venkatbabu1864 жыл бұрын
Multiplication is a surface ratio of radius. Since it is a constant you can use it for waves production groups. Waves conversions in higher dimensions are a constant times a lower dimension.
@HelloKittyFanMan.4 жыл бұрын
Ha, for a second I thought, "Ohhh, here we go, here comes the calculus!"
@mrshappymon2 жыл бұрын
Thank you. Can this method be used to proof the area of other shapes like rectangles and square?? ( I tried and it did worked on square, but not with rectangles neither regular hexagons) If this cannot be used in this shapes can you explain why?. Sorry, if the answer is obvious, thank you. Your videos are amazing to watch. 😊
@cosmogamer99144 жыл бұрын
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
@HelloKittyFanMan.4 жыл бұрын
Yep, the difference in teaching quality can EQUATE (haha) to a similar difference in learning quality.
@kalpeshsanatani3 жыл бұрын
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..
@HDitzzDH5 жыл бұрын
0:16 Thought someone stepped on a dogs paw or something wtf.
@Sarah-zb5 жыл бұрын
GZA 🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣
@stevethea52504 жыл бұрын
@@Sarah-zb Paying for accommodation Please provide details about how you pay for your accommodation. You must answer all questions unless they are marked optional. Do you pay fees for your accommodation?This includes rent, board and lodgings, site fees or any other fees. Yes No This is asking if you pay something for the right to stay in the place you live. Click here to launch the digital assistant Do you get free accommodation? Yes No This is if you don't pay for the place you live in. Click here to launch the digital assistant How would you describe your current accommodation circumstances? Please be as specific as possible. Click here to launch the digital assistant Press "Continue" to save your changes and proceed You will have a chance to review these details later and make changes if needed.
@rahulkulkarni32384 жыл бұрын
🤣🤣🤣
@JustinHyneswashplant264 жыл бұрын
I am in calc 3 and I am still amazed at what I am learning from videos like these. Keep on going.
@johannschiel67344 жыл бұрын
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.
@ianjamesbarnett5 жыл бұрын
Love the idea behind the proof. Cool concept. However you didn't prove that the stretched out consecutive rings are increasing linearly in length. This of course follows from circumference being a linear function of radius, but to be rigorous it does deserve mention.
@GiantSuperZombie4 жыл бұрын
I agree, this was skipped a little to quickly. It being circles you could easily imagine it to be something like part of a sine wave or a parabola. So it is rather important to show that the lengths increase linearly, else you wont get a straight hypotenuse and you cant describe the area as a triangle.
@pasikuisma85052 жыл бұрын
@@GiantSuperZombie He did proving it by drawing a line through. That is proving the lengths increase linearly.
@Scarsofevil4 жыл бұрын
When I was in school, I was just given an equation
@rjningthouja5733 жыл бұрын
More teacher like you need in our country the way of explanation is more clear than package bottle 🍼🍼🍼🍼🍼🍼
@cangjie126 жыл бұрын
Did you just show a visualization of differentiation? When you differentiate area you get circumference..
@dhavalpahadia133 жыл бұрын
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.
@krish67295 жыл бұрын
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.
@ney17adi3 жыл бұрын
He is so awesome man... His way of teaching is lobb😍
@FinetalPies6 жыл бұрын
This is why geometry is so important, formulas in algebra all have reasons behind them
@hotflashfoto3 жыл бұрын
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!
@rossithomas24156 жыл бұрын
Question: A circle of diameter 1. Considering that pi is a irrational number, does the circumference ever loop back on itself, or does it tend to close at Infinity only such as there's never ever such a thing as a closed circle ?
@salutoitoi6 жыл бұрын
Very good question. Maybe I won't respond your question but here is my point: I think that mathematics have been invented to explain the world in which we live and we know that infinite things are mindblowing (did you ever see infinity ?). That's why we created the notion of significant figures where we only take things that can be "finite". For usual uses, 3.14 is enough but maybe for some work where a physicist/scientific works with microns sizes, it won't be enough so you'll have to use more precision and fortunally PI offers you that.
@dinopad106 жыл бұрын
I have a thought on that question... if not necessarily a satisfactory answer! When we look at the real world, as salutoitoi suggested, we never actually have a closed relationship. For instance, at the atomic level, everything that exists, including you and me, actually has space between every atom. There are only electromagnetic forces that hold us together. So, likewise, a circle of a diameter 1 never closes, but gets to an infinitely smaller distance, just as pi gets infinitely smaller, the further from the decimal we calculate. So, I suppose that technically, a circle is actually just a perfectly curved line segment that infinitely, but never ultimately, approaches closure.
@Bananananamann6 жыл бұрын
Yes, it will loop back on itself, according to the definition of continuity. For every epsilon I pick, I can compute pi as exactly, so as to make the gap smaller than that picked epsilon. In other words: The "real" length would be exactly pi. We cannot compute pi, so we take an approximation that is smaller (We could also make the approximation bigger). Now, there is an error. However I can reduce that error at my will, by computing pi more exactly. For every value that I can imagine, I can make the error smaller than this value. This means, that the line would be continuous.
@HritikV6 жыл бұрын
Irrational numbers are NOT weird numbers. You can plot them as precisely as you want. Same applies with real numbers 2.0000......
@Ougagagoubu6 жыл бұрын
I'm late but I think the number pi does not work like that. The circumference does loop back on itself after exactly pi*D It is irrational because of the curvature of a circle, wich can't be described by another number. But that doesn't mean that it is a number that can't be shown or reproduced in the real world. Just like a square with the area 2. It's sides are sqrt(2) long, wich is irrational. But it is just that. Very weird to explain but not as weird if you see it drawn on a peace of paper.
@Dalton12946 жыл бұрын
Another way to write the area of a circle formula is A=C^22/4pi. I learned this in pre-calc and how to derive the formula. r=C/2pi, solve for r using C=2pir A=pi(C/2pi)^2, substitute C/2pi for r A=pi*C^2/4pi^2, (a/b)^n=a^n/b^n A=C^2/4pi, the pi and pi^2 terms cancel leaving one pi term left OED
@geetargato6 жыл бұрын
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.
@gabrielmello32936 жыл бұрын
What's so impressive about it? This is the basics of greek geometry.
@nicholass39645 жыл бұрын
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.
@mazeltov21104 жыл бұрын
Awesome 👏🏻, he just explained the area of circle and integration in so beautiful way. 🙏🙏🙏
@henkeball4 жыл бұрын
You didnt explain why putting slices between each other draws a straight line and not an exponential line growth
@apocalypticbean4 жыл бұрын
because circumference is directly proportional to radius
@dazaisan66972 жыл бұрын
wow.. amazing.. just simple concept but never crossed my mind. wow😮😮.
@usmanmushtaq53104 жыл бұрын
00:17 gosh that sneezed scared the hell out of me!
@rafaelalemke3 жыл бұрын
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.
@vedantdinkar96824 жыл бұрын
I just realized... *THE CIRCUMFERENCE OF A CIRCLE IS THE DIFFERENTIATION OF ITS AREA WITH RESPECT TO R.*
@jatinkamal27554 жыл бұрын
its not exactly a gradient...
@veyselyazici4 жыл бұрын
Dear Mr Woo, I take the whole circle as if it is a triangle with base 2piR and height R. Result is the same. The same formulation can be used to find the area of a slice, (arc length times radius)/2.
@FieldWren4 жыл бұрын
Watching this while knowing integration and only connecting at the beginning that PIxr^2 is the integral of 2PIr
@siang10043 жыл бұрын
Thanks for clearing my doubts in just a simple way, nice teaching!
@nexusclarum80006 жыл бұрын
decimeters. underrated unit of measurement. fun fact: 1 cubic decimeter = 1 litre
@SaurabhKhatri214 жыл бұрын
Really good video... Enjoyed it thoroughly
@ChapCanai5 жыл бұрын
This guy has both knowledge and understanding, unlike most teachers who only have knowledge
@ValidatingUsername5 ай бұрын
I think cutting the circle surrounded by a square into for quadrants and rationalizing the r^2 is a quadrant then multiplying by the pi scalar instead of 4 would help a lot of people.
@TheZombiecowmeat3 жыл бұрын
I've been through endless amounts of math classes in my lifetime, and never has anyone every told me the WHY.
@tc18173 жыл бұрын
You're full of shit. Any high school math teacher can tell you where pi comes from. What exactly were your questions?
@TheZombiecowmeat3 жыл бұрын
@@tc1817 "can" tell you, sure. "Did" tell us, no.
@tc18173 жыл бұрын
@@TheZombiecowmeat You didn't ask.
@TheZombiecowmeat3 жыл бұрын
@@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
@tc18173 жыл бұрын
@@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?
@matteo78614 жыл бұрын
a beautiful way of teaching integration without naming it ! Bravo !
@yxungatlas6 жыл бұрын
dat sneeze holy shit
@yuzuruotonashi42346 жыл бұрын
A sneeze and a half*
@MrAnperm6 жыл бұрын
Sneeze^2
@darkknight98035 жыл бұрын
(Sneeze)^2+-(Sneeze)^2 Solve for S.
@mulac16262 жыл бұрын
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
@CorekBleedingHollow4 жыл бұрын
We definitely need more Asian math teachers in our schools. That's a compliment.
@ChuddmasterZero4 жыл бұрын
That was awesome. Never seen that proof and it is wonderfully elegant. Also props Eddie - that first circle you drew was amazing for freehand!
@vpsjdon4 жыл бұрын
00:20 Weird to think that that sneeze would've been a much bigger deal had it happened these days
@subashsankar80195 жыл бұрын
I am not a maths student. But I am quite sure that I am not allowed to cancel the 2s in r+2pi.r/2 it would be r/2 + 2pi.r/2= r/2 + pi.r= r+2pi.r/2. Correct me if I am wrong
@thomasquint59065 жыл бұрын
its not a plus, the formula for the area of a triangle is the (base * height)/2. so, that's why he cancel the 2.
@jacinth89935 жыл бұрын
tbh that circle may actually be close to 2m, but just may not look like it
@igoretski5 жыл бұрын
6:30 the pizza solution. You start with 4 pieces, and you fit a triangle in each of the 4 quarts of the circle. Then you go to 8 pieces, 16 pieces and so on (always the double) and the smaller the pieces get the closer the triangles fit into the circle parts. Now it might be a little cumbersome to calculate the height and baseline of these fitting triangles. We can take different triangles, as long as they approach the circle parts, when they get smaller and smaller slices. In a very small slice you can say that the height of the triangle is almost the radius r, and the baseline is 2πr divided by the amount of slices. Starting with 4 pieces, each of the triangles has 2πr/4 baseline and height r. So the area of each triangle is 2πr/4 * r * 1/2. (1/2 because it's a triangle and not a square). Now you have 4 such triangles, so it's 4 * 2πr/4 * r * 1/2, and for 8 pieces it will be 8 * 2πr/8 * r * 1/2 and for n pieces it will be n * 2πr/n * r * 1/2. If you shorten that it becomes obvious that you can remove the n's, which gives 2πr * r * 1/2 and then you can also remove the 2's, which ends up in πr * r or πr².
@asmedeus4483 жыл бұрын
Thanks for the explanation. It really helpful.
@hazelnutsheep78636 жыл бұрын
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.
@suhailmall986 жыл бұрын
*when I need the circumference
@hazelnutsheep78636 жыл бұрын
@@suhailmall98 my bad, fixed it
@eloquexquisite31035 жыл бұрын
I REMEMBER THIS
@liamcraddock95395 жыл бұрын
Apple pies are square (A= pi X r^2)... cherry pie delight (C= pi X d ) is how I was taught it 😂😂
@joebaker38223 жыл бұрын
Got a kid in school learning this stuff. Excellent refresher so I can help him when he asks. Thank you.
@buddhurambaske56256 жыл бұрын
Hey Eddie! We can also find the area of circle by integrating the circumfernce of that circle.
@dhy53426 жыл бұрын
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.
@TheHiddenChronicle-b9l5 жыл бұрын
@@dhy5342 no you actually cant. You messed up slightly on your calculations.
@outissituo22695 жыл бұрын
Mr Woo, please comment: why do the tops of strips in your stack form a "hypotenuse" of triangle? Why do the tops form straight line? Why isn't it convex line up or down? Then the formula for area of triangle would not be applicable. You use proportionality implicitly. Why not to mention that the length of stripe is 2𝜋r so proportional to r? By the way, I've always thought the area of circle is ZERO. The area of DISC of radius r is 𝜋r^2.
@shinnyii4 жыл бұрын
Dead classroom, I verbally said “wow” when he finished the proof. Where’s the enthusiasm lmao
@WouterZtube3 жыл бұрын
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.
@9Joel94 жыл бұрын
Everyone is talking about the nicely drawn circle, but I'm here exstatic he's introducing the metric system to the english speaking world.
@internetguy24574 жыл бұрын
Australia is metric
@dragonf1y033 жыл бұрын
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.
@imie-nazwisko6 жыл бұрын
When you realize you never gonna slice a perfect 6 pizza pieces because pi ruined it.
@pasijutaulietuviuesas91746 жыл бұрын
Fullus Retardus But you'll never get a perfect pizza in the first place because of the same reason.
@yarubik6 жыл бұрын
He Who Judges oh shit
@jonatangarcia92856 жыл бұрын
Of course you can a pizza with (Pi*r²)/6 area of slice of every pizza piece
@vinodkumar-wm3oq5 жыл бұрын
The good thing is, it is made of atoms. Yes people, finite, rational and beautiful (just don't bring the quantum mechanics guys) ;)
@baldyslapnut.4 жыл бұрын
You'll get 6.283 slices I'd wager.
@m1m7604 жыл бұрын
The height of the last (outer most) strap should be 2(pi)r and the total length at the bottom should be r---This is obvious. The perpendicular and the base should be straight line---that I understand. But the point is, why should the other side has to be an acceptable straight line, not a noticeable curve? If area is (pi)r^2, then we may conclude that it should be a straight line to make a triangle, not the other way round.
@johndawson60574 жыл бұрын
Imagine being so bored out of your mind you click this video and read my comment.
@saynotop2w4 жыл бұрын
Ya got me, an ADHD patient
@rudnickulous3 жыл бұрын
Wasn’t there an assumption that the function is linear and therefore the area is a triangle? We know the limits are 0 and pi*d, but if I didn’t know the answer already it wouldn’t be apparent to me that I should be able to assume that a straight line connects those 2. Can anyone explain this?
@Dark3nedDragon5 жыл бұрын
I feel that it helps to put the video on speed 1.5
@SeventhCereal3 жыл бұрын
These videos do a great disservice. The results are known a-priori and an imprecise line of reasoning is made to match the known result. The fact is if one cannot precisely deduce the result then one lacks the proper tools and should WORK to obtain the tools rather than vainly searching for youtube parlor tricks.
@keshav5676 жыл бұрын
Yes good but who's gonna prove C = 2πr ? I need to know that too
@mklinger235 жыл бұрын
π is defined by C/D. That's just a fact that we get to use. So therefore C=π*D if you multiply both sides by D. Then we also know that the radius is 1/2 of the diameter so D=2r so if you plug that back in to the beginning you get C=2πr
@FFF666GP5 жыл бұрын
Pi is a constant, the definition of which is based on the realisation (by some astute observer) that for every circle, C/D is the same. The elegance of denoting it by a symbol or abbreviated name is that one does not have to evaluate it numerically while performing symbolic computations/manipulation
@albertoolmos213 жыл бұрын
Instead of stripes, you can use small circular segments (triangles) of sides R and base B. Thus, the area of each triangle is R*B/2. Knowing that a complete round of B (the circle) is 2*Pi*R, then A = R*(2*Pi*R)/2 = Pi * R^2.