Area of a circle, formula explained

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  • Опубликовано: 30 дек 2024

Комментарии • 1,8 тыс.

  • @tj8870
    @tj8870 8 лет назад +3147

    This is real mathematics, real understanding.

    • @fr3fou
      @fr3fou 6 лет назад +8

      Angular

    • @fr3fou
      @fr3fou 6 лет назад +5

      React

    • @NikoCubeRoot
      @NikoCubeRoot 5 лет назад +4

      a colon is :

    • @missionpupa
      @missionpupa 5 лет назад +24

      Mathematics is found in insight, and not in computation. Forgot the mathematician who said that.

    • @MrCalist3r
      @MrCalist3r 4 года назад +46

      Why do schools skip true understanding? math classes today are just; here’s formulas! and rules! now put these 100 problems into your calculators.

  • @exhalerwolf1272
    @exhalerwolf1272 4 года назад +549

    For anyone wondering where 2πr came from, π is DEFINED as the ratio of the circumference to the diameter of a circle, π = circumference/diameter
    diameter = 2 x radius = 2r
    So, circumference/2r = π
    Multiply both sides by 2r and you get
    Circumference = π x 2r or 2πr
    This is not proof or anything, just the fact that π is a special number and a ratio and also an irrational number (cause the ratio of two rationals would never produce an irrational, one of them must be irrational, in this case it's the circumference. Hence it must have π in it's formula)

    • @uncleteam
      @uncleteam 4 года назад +12

      EXHALER Wolf Still begs the question how to measure the circumference? The whole purpose I thought was not to have pie 🥧 in the final conclusion. 🎰

    • @exhalerwolf1272
      @exhalerwolf1272 4 года назад +29

      @@uncleteam A circle is effectively a polygon with infinite sides. First values of π were measured with polygons that had stupid amount of sides. So no matter how many sides you add, you can never truly 'measure' the circumference of a circle. There will always be error. So the best way is to define a ratio of the total perimeter to the longest diameter as some number (π) that approaches a value 3.14159... but never ends or repeats itself.
      So the best way to measure circumference of a circle is to measure a quantity that is rational, therefore can be measured with much more greater accuracy, the diameter or radius and use the appropriate formula to get an accurate enough result. Numberphile concluded that only 39 digits after decimal of π is needed to calculate properties of a circle/sphere of size of the known universe with an error comparable to the diameter of a hydrogen atom. Yet our computers have calculated up to trillions of digits after decimal.

    • @brain0nfire
      @brain0nfire 4 года назад +13

      It's so intuitive when you use a piece of string to surround the circle and as you spin it into a straight line you just compare to the diameter to realize it's ~=3.14 bigger. The string makes it so practical, you barelly need numbers to work it out, as long as it is proportional.

    • @alvarogoenaga3965
      @alvarogoenaga3965 4 года назад +9

      You still have to demonstrate that the ratio between the circumference of ANY circle and its diameter is a constant (π).

    • @hafizzhg
      @hafizzhg 4 года назад

      Thanks i need that

  • @thamestrinity
    @thamestrinity 9 лет назад +1451

    clear explanation + wonderful animation = perfect video!

    • @owen429
      @owen429 9 лет назад +1

      Quỳnh Huỳnh I agree

    • @manasjoseph395
      @manasjoseph395 9 лет назад +1

      Quỳnh Huỳnh agree

    • @Croftice1
      @Croftice1 7 лет назад

      +undo.kat you can say, where the base came from, since he compared it with the circle. And you can say, where Pi came from, since everybody learns it in school. You really want the proof of Pi? Ask your teacher about it, since things like Pi, e, Sin, Cos, Tan and co are constants, that no one dares to doubt. lol

    • @anyamram
      @anyamram 6 лет назад +1

      Nice explanation

    • @pianoplaynight
      @pianoplaynight 4 года назад +1

      + Beethoven music in the background 😊

  • @retiredtom1654
    @retiredtom1654 4 года назад +308

    I wish that teachers explained it in this way when I was in school. This explanation was very clear... Thanks!

    • @mr.schloopka1124
      @mr.schloopka1124 4 года назад +3

      We did this and it was in the book as well

    • @Minuey
      @Minuey 4 года назад +3

      @@mr.schloopka1124 i never learned this until now. Im currently taking calculus 2. more often than not 2 year olds would compare the 4 corners of a square and add up its angles, 360°, to a circle, and jokingly say "sEe? a SquaRe iS eqUAl tO a CiRCle"

    • @harshitpankaj8419
      @harshitpankaj8419 2 года назад +1

      @@mr.schloopka1124 yes this was in book but not in this manner

    • @irish3353
      @irish3353 10 месяцев назад +2

      Interestingly, this is basically a calculus approach to the question. Take the integral of the circumference to get the area.

  • @philburch1970
    @philburch1970 4 года назад +367

    Why the HELL didn't they teach the basis of things like this in High School. It is so much easier to understand the formulas when you can see where they come from.

    • @MSloCvideos
      @MSloCvideos 4 года назад +30

      They did, though. What he is doing is using limits to get a definite integral.
      This is all done in highschool, it's just not animated like this.

    • @andrewqzx3830
      @andrewqzx3830 4 года назад +55

      MSloCvideos wasn’t for me, teachers just tell u it’s pi(r^2) and that’s it, I’ve never seen an explanation before RUclips

    • @poopswagtyrone7543
      @poopswagtyrone7543 4 года назад +41

      @@MSloCvideos no, teachers tells you the formula, but doesn't explain how you get the formula, which makes it confusing for students.

    • @vascomanteigas9433
      @vascomanteigas9433 4 года назад +13

      @@poopswagtyrone7543
      This video replicates the original proof given by Archimedes.

    • @keksitzee1094
      @keksitzee1094 4 года назад +27

      @@MSloCvideos - Sounds like you had a teacher that cared to explain why. Many people don't have such thorough teachers.

  • @NoosaHeads
    @NoosaHeads 5 лет назад +63

    An elegant, simple and entirely understandable description.
    If I'd had you as my teacher, all those years ago, I'd probably have ended up as a mathematician.

    • @CStrik3r
      @CStrik3r 4 года назад +5

      And this is what pisses me off about modern education

    • @gabrielrabelo6982
      @gabrielrabelo6982 4 года назад +1

      @@CStrik3r care to explain the other flaws you perceive, as well as your solutions/ideal scenarios?

    • @gaaraio2771
      @gaaraio2771 2 года назад

      @@gabrielrabelo6982 teachers vomit formulas and concepts like it is all but a memory game. True learning and understanding comes from logic. Without rational discourse no learning is taking place. But more important than rational teachings is to encourage the student to become an active learner. They must learn how to learn - that is, to seek the truth behind the theoretical framework of readily available conclusions (instead of becoming satisfied with knowing the formula of the area of a circle, to learn the process behind it by their own volition and curiosity, for example). That way, I believe the average student could likely finish learning effectively the entire curriculum behind their college major three to four years earlier than it is expected today (they would already finish highschool content before the age of 15, and finish the equivalent content of a college major by the same time someone today would start college). Sal Khan did exactly that when he was accepted into MIT - in 4 years he completed a triple STEM major in math, CS and electrical engineering by not going to any class at all and just learning by himself through the books. The degree of time effective study an active learner holds just makes for a far better use of their time spent studying than a passive student who keeps expecting to be spoon-fed the knowledge from your usual school and college classes. I myself enrolled in a top business school but I never tried to pick up the reference material up until the last year in college. I started reading from start to finish the main bibliography before the scheduled classes, and kept reading the material instead of attending, and in a week I could cover the whole content from 100 hours of classes and beyond. Many others who lived a similar experience to mine can attest to my following statement - that is, 4 months is more than enough for an active learner to cover the whole finance major, instead of the scheduled time of years.

    • @imhopelesslyaddictedtofent4266
      @imhopelesslyaddictedtofent4266 2 года назад

      @@gabrielrabelo6982 ⬆️

    • @teixopoison601
      @teixopoison601 2 года назад

      @@gaaraio2771 brasil é assim mesmo

  • @faziranoor
    @faziranoor 8 лет назад +282

    This made me understand maths like 10000000x better THANK YOU

    • @9b.12.jagatjibanparida6
      @9b.12.jagatjibanparida6 6 лет назад

      niceeeeeeeeeeeeer video

    • @dekogg
      @dekogg 4 года назад +1

      I read: this made me understand maths 100000x better THAN you. lol

    • @seeseefok7659
      @seeseefok7659 4 года назад +2

      @@dekogg lmao, don't think maths as a competition my dude, think it as a topic that we can all share joy with each other

  • @malejeeck
    @malejeeck 4 года назад +330

    2011 YT: people aren't ready
    ..
    ..
    ..
    2020 YT: the time has come!

    • @maxhaibara8828
      @maxhaibara8828 4 года назад +3

      Because of online class

    • @Until_It_Is_Done
      @Until_It_Is_Done 4 года назад +5

      Your account is only 5 years old. How would you even know if it was recommend in 2011 or not? 🤦🏾‍♂️😂

    • @bounyh508
      @bounyh508 4 года назад +3

      @@Until_It_Is_Done Account was made in 2010. You can check view velocity using Vid IQ. or are u indians too poor to afford that shit?

    • @Until_It_Is_Done
      @Until_It_Is_Done 4 года назад +3

      @@bounyh508🤦🏾‍♂️ click on his name ya idiot! it says "joined 5 years ago". 😂😂 so Tabby boi, are you stupid or just stupid? 🤭

    • @user-bh6cz8kp4q
      @user-bh6cz8kp4q 4 года назад +1

      @@Until_It_Is_Done Jesus, are you stupid? It litteraily saids video made in 2011. Are you blind or stupid? Probably both.🙄🤦‍♂️ Did your parents drop you om the head when you were a kid?

  • @CiRdy34
    @CiRdy34 Год назад +3

    3 minutes, easy to follow for anybody, voice is crystal clear, video graphically helps with understanding… 11/10 video.

  • @nuke1210
    @nuke1210 4 года назад +30

    2019: memes
    2020: memes and a little bit of math

  • @toiletpaper3536
    @toiletpaper3536 4 года назад +75

    My whole class found it so satisfying how the triangles just for perfectly together xD

    • @alvarogoenaga3965
      @alvarogoenaga3965 4 года назад +3

      I know, right. Like the proverbial puddle of water fitting into the pothole.

    • @chillshobe8147
      @chillshobe8147 4 года назад +3

      They showed this in your class? Lucky bitch

    • @joselimon5181
      @joselimon5181 Месяц назад

      My class did too, it was smooth

  • @cesarbuenobustamante5301
    @cesarbuenobustamante5301 4 года назад +3

    I solved it with other way. I found a formula to the area of every regular polygon, adding the areas of the triangles that the polygon is made of. The result: A=d*b*n/2, where (d) is the distance between the centre of the polygon and the centre of one side; (n) is the number of sides; and (b) is the lenght of the side. The area of a circle would be the limit of that formula when (n) tends to infinite, b would be the circunference split for the number of sides, and d would be the radio. If you solve that limit, the answer will be pi*r^2. Sorry if my english isn't good, I'm peruvian. Good video!.

  • @CombaOsu
    @CombaOsu 8 лет назад +760

    But he used comic sans

    • @i_found_bacon5561
      @i_found_bacon5561 8 лет назад +7

      Lol

    • @howtungchong174
      @howtungchong174 8 лет назад +18

      why using comic sans is wrong

    • @Zack-xz1ph
      @Zack-xz1ph 6 лет назад +11

      comic sans is just tacky, if you still like though I recommend "Comic Neue", it's a more professional looking comic sans

    • @rurukado
      @rurukado 6 лет назад +6

      I find this hillarious bcs my math teacher uses comic sans when making our test paper lolol

    • @sudhachoudharychoudhary6784
      @sudhachoudharychoudhary6784 6 лет назад

      Fckk

  • @preetijadhav6574
    @preetijadhav6574 4 года назад +25

    Had I learnt math this way in school..I would have been an physicist.. Absolutely easy to grasp...Fantastic.

  • @jamminoutrexan5474
    @jamminoutrexan5474 9 лет назад +10

    Thank you so much! The animations helped with the explanation, and the explanations were spoken at a good rate. I admittedly had to rewind the video at about 2:24, but after that, got the concept clearly. Great video!

  • @lodgechant
    @lodgechant 7 месяцев назад

    Watching - and working through - your elegant, accessible video was exhilarating. It took me about 15 minutes of noodling around on a piece of paper, exploring your ideas, and I now finally understand in a very pragmatic way the fundamentals of the relationship between pi, circumference, diameter, radius and area. A thousand thanks!

  • @ap-pv7ug
    @ap-pv7ug 4 года назад +4

    The beautiful thing about this is, the mathematically rigorous way of solving this question using integration is essentially the same thing. What you did at 1:05 is exactly what a Riemann sum does.

  • @mrjhdsb
    @mrjhdsb 2 года назад +3

    the kids in my class love this video. You are the greatest youtuber of all time. the end

  • @sunitavyas8570
    @sunitavyas8570 Год назад +40

    Any legend here watching after 12 years 🤣🔥

  • @archivaldogutierrez7439
    @archivaldogutierrez7439 10 месяцев назад +2

    My god pure gold !!! 😮 I was forced to learn the formula , but i coudnt understand where it came from , many thanks for this eye opening class

    • @dsavoy66
      @dsavoy66 10 месяцев назад

      Las demostraciones geométricas son un lenguaje simple y visual que acompañan a la demostración matemática que es más abstracta y compleja de entender , dándole apoyo a su comprensión y sobre todo a su aplicación práctica en el mundo físico

  • @KarRebWil
    @KarRebWil 12 лет назад +5

    This is such an excellent explanation of the Area of a Circle. I show my classes this video each time I teach this topic. Thanks a million!

    • @harishkulkarni7244
      @harishkulkarni7244 Год назад +1

      You're a good teacher if you are looking up how to explain the area of circle to students! I knew the formula but wasn't sure how we arrived at the formula so this video explained it very well. Good luck.

    • @Dubdubwubbalubba1
      @Dubdubwubbalubba1 2 месяца назад

      What a good teacher

  • @wangshuoleon4400
    @wangshuoleon4400 4 года назад +5

    I learnt this when I was pupil, I still remember the teacher told us use the scissor to cut the circle. A few days later, she brought a cylinder, broke into pieces and combine to a brick. Teaching us how to compute the volume. I have to say the scientific education is so great in China before university

  • @spicedkitcat
    @spicedkitcat 4 года назад +26

    bro our math teacher sent us here
    when the teachers get tired of sh!t

  • @someonep3313
    @someonep3313 3 года назад

    Dude your the only man that can use a simple voice and music and get me so amazed and invested into math LIKE BE MY TEACHER PLZ

  • @jennievan7844
    @jennievan7844 8 лет назад +13

    Thank you so much! This was so helpful and I got it right away! Your explanations are very clear

  • @sekimpiderrick1053
    @sekimpiderrick1053 6 месяцев назад

    This is the clearest explanation u can get online.
    Thanks

  • @stanleycates1972
    @stanleycates1972 2 года назад +7

    All my years I have taken these wonderful formula for granted. Understanding the hard work done in early times is very interesting and would help understanding calculus down the road.

  • @vaasukrishnan8321
    @vaasukrishnan8321 2 года назад

    The best explanation for area of circle I have ever seen. The perfect animation is cerry on top.

  • @macdermesser
    @macdermesser 6 лет назад +5

    Nice. Is there a similar way to envision the formula for the circumference, which you use to get the area formula?

  • @sarinaisnain8116
    @sarinaisnain8116 5 лет назад +1

    Area of circle: π x radius x radius
    Area of semicircle: 1/2 x π x radius x radius
    Area of quadrant: 1/4 x π x radius x radius
    Circumference of circle: π x diameter
    Perimeter of semicircle: π x diameter
    Perimeter of quadrant: π x diameter
    Am I right?

  • @jacoblamothe989
    @jacoblamothe989 5 лет назад +6

    This video literally brought me to tears. Something about deriving the area of circle makes me remember the time I spent with my mother when I was little.

    • @calvinlee1127
      @calvinlee1127 4 года назад

      Who got a bigger slice of pizza than?

  • @edmondtt
    @edmondtt 3 года назад

    This presentation is clear and cool! This is much more important than applying the formula repetitively without knowing the proof in school..

  • @alburnto
    @alburnto 5 лет назад +3

    Damn! Thank you, I was mistaking the circumference of the circle for the base. Appreciate the effort and clear explanation.

    • @vadkaa5053
      @vadkaa5053 5 лет назад

      You can do that (base= circumference) but then ur height will be quarter of the diameter (D/4)

  • @pigeonfun1771
    @pigeonfun1771 Год назад

    OMG. This video was amazing! It cleared my doubts. The animation must have taken so long. And, it is so useful. Thank you so much for the help! Keep up the good work!

  • @jennaestep6179
    @jennaestep6179 7 лет назад +5

    Thank you so much. This helped me understand one of the topics for a test a lot more than I did before. Great video!

  • @arnoldrimmer9161
    @arnoldrimmer9161 6 лет назад

    Superb visualisation for people who struggle with the 'standard way' of doing math. Well done love it!

  • @roygbiv176
    @roygbiv176 10 лет назад +13

    it is easier to understand the area as the addition of all of the circumferances of smaller circle within it: the intergral of 2pie*r with respect to r. but still great video and great channel

    • @neurofiedyamato8763
      @neurofiedyamato8763 5 лет назад +7

      No, that is not easier to understand. That requires calculus which many find rather difficult. This video can be shown to a middle schooler and they would understand it. So this video is easier to understand

    • @theodiscusgaming3909
      @theodiscusgaming3909 4 года назад

      @@neurofiedyamato8763 that is calculus but not really, what you end up with is a right triangle with base R and height 2(pi)R. You just have to calculate the area based on this.

    • @MSloCvideos
      @MSloCvideos 4 года назад

      @@theodiscusgaming3909 how do you prove that the area of the triangle is indeed the area of the circle?

    • @theodiscusgaming3909
      @theodiscusgaming3909 4 года назад

      @@MSloCvideos same as the video. The collection of rectangles approaches a triangle as they become smaller and smaller.

    • @MuffinsAPlenty
      @MuffinsAPlenty 4 года назад

      @@MSloCvideos You don't. It's an assumption. Or rather, it's a definition. What does the area within a curved region mean? We _define_ the notion of area in a curved region so that this method works. This is an extremely reasonable definition because of what AyyMD VEGA said - we can see that as we increase the number of triangles we use, our intuition of what the error is gets arbitrarily close to 0. We just say, then, that this is what area means.

  • @vibhakumari2152
    @vibhakumari2152 4 года назад +2

    WOW...THE WAY YOU PRESENTED THE VIDEO IS AMAZING....👍🏻👍🏻:)

  • @Amitsahu12340
    @Amitsahu12340 4 месяца назад +33

    Who is in 2024

  • @jamesdesantis9420
    @jamesdesantis9420 8 месяцев назад

    Thanks so much - great video! I've seen this argument in textbooks, but this video is so much better. I'm a teacher and I showed this to my geometry class - it made it very clear to them!

  • @sigmabond1289
    @sigmabond1289 9 лет назад +40

    dis was really gr88!!! I wish ppl kept making such wondrful vids

    • @mzg147
      @mzg147 9 лет назад +7

      +ishan bhange I wish you improved your spelling.

    • @wilhufftarkin8543
      @wilhufftarkin8543 5 лет назад +1

      Dis was really greightyeight?

    • @pesto9186
      @pesto9186 5 лет назад

      Bruh too many abbreviations. Just use normal English

  • @lunairenic
    @lunairenic Год назад +2

    thank you so much, you taught me more than all my math teachers. honest.

  • @yohannesyebabe7923
    @yohannesyebabe7923 5 лет назад +3

    p*r^2= 2*integral (sqrt (r^2-x^2))dx from -r to r.
    This complets the proof!

  • @MithunNath-ih6ti
    @MithunNath-ih6ti 2 месяца назад

    I love your channel so much, and you!!! May God bless you!❤🎉

  • @AnisurRahman-hf8mw
    @AnisurRahman-hf8mw 4 года назад +27

    I discovered this same idea independently when i was at 16 years old in my own interest. I am happy to see this video today. Unfortunately now i am a medical student due to my parents interest!

    • @stuffido1536
      @stuffido1536 3 года назад +4

      @Bantai Rapper lol, you just had to one up this guy. Were you jealous of him or something?

    • @featherycoffee1401
      @featherycoffee1401 3 года назад

      Indian, makes sense

    • @el6ment0
      @el6ment0 2 года назад

      @@stuffido1536 pretty sure hes joking lol

    • @IsaacAsimov1992
      @IsaacAsimov1992 8 месяцев назад

      The world needs good doctors.
      Glad you went the medical rather than academic math route.

  • @_J_i_N_x_s_u_r_p
    @_J_i_N_x_s_u_r_p 10 месяцев назад

    I've never had anyone explain it this way, this is too good

  • @Henil-S-Mokani
    @Henil-S-Mokani 2 года назад +3

    It can also be like - Area of a Circle = Area of a parallelogram = base × height = 2(pi)r/2 × r = (pi)r × r = (pi)r² . It is good for making models because dividing in smaller parts is harder.

    • @yiutungwong315
      @yiutungwong315 Год назад

      ❤😂🎉😢😮😅😊

    • @yiutungwong315
      @yiutungwong315 Год назад

      π = 2 in Riemann Paradox And Sphere Geometry Mathematical Systems Incorporated...

  • @RM-sy8oo
    @RM-sy8oo 4 года назад

    the thing i like most about this video is that you don't need the audio to understand it, the visuals are enough

  • @pratapmistry7659
    @pratapmistry7659 2 года назад +5

    Man biggest mistake of my life is watching these videos after 11 years ...🤯🤯

    • @DeshBhakt-t3c
      @DeshBhakt-t3c Месяц назад

      Why? Is it possible that you have lost everything just like me? 😁

  • @venkattex1
    @venkattex1 3 года назад

    Excellently explained. My kids learnt in a minute. Many Thankx.

  • @MegaMoh
    @MegaMoh 4 года назад +3

    All people here saying pi by definition is the circumference over the diameter but no one is mentioning a proof or reason why that ratio is constant :/

    • @MegaMoh
      @MegaMoh 4 года назад +1

      @dalia rosstom I can't just "define"(a very overused abused term) a number to be the ratio between the length to width of a rectangle. There isn't just 1 ratio; a rectangle can have lengths and widths with different ratios relative to one another. Why wouldn't the circle be different? You should prove that the ratio of the circumference to the diameter is always constant.

    • @deezem5294
      @deezem5294 3 года назад

      @@MegaMoh The radius of the circle is always the same

    • @deezem5294
      @deezem5294 3 года назад

      @@MegaMoh pi couldn't change. It will be different only if radius is different. However, that will not longer be a circle, as the definition of circle is "A circle is the set of all points in a plane that are *equidistant* from a given point called the center of the circle"

    • @deezem5294
      @deezem5294 3 года назад

      @@MegaMoh definition of rectangle: "In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle."
      It only specifies the angle, not any ratio or dimensions. So you can push and pull until length to breadth is 31469420^31469420:1^-1000
      but it would still be a rectangle if its angles were the same.

    • @MegaMoh
      @MegaMoh 3 года назад

      @@deezem5294 you can make a rectangle that has a side's length equal to 5 and then change the other side's length. So it is possible to have a 5x2 rectangle, a 5x3 rectangle, a 5x4 rectangle, a 5xN rectangle where N is just any number. You should prove that a circle with a radius = 5 can not have a circumference of different lengths and can only have 1 length. That is an assumption that you should prove.

  • @pinaymathteacher1288
    @pinaymathteacher1288 3 года назад

    I prefer your presentation because it is done slowly and this is how i also present this lesson in class especially for elementary students.

  • @davidprock904
    @davidprock904 4 года назад +3

    Bleeping Love it, explained Flawlessly Perfect !

  • @richardwallinger1683
    @richardwallinger1683 3 года назад

    wow you made that sound so darn easy .. excellent narrative . 76 years old and still learning stuff.

  • @xddtherat
    @xddtherat Год назад +4

    pizza on school parties:

  • @Amb3rjack
    @Amb3rjack Год назад

    Utterly magnificent explanation and easy as pi to understand . . . . . . (Sorry, couldn't resist, even if it has been said hundreds of millions of times before)

  • @nameless4630
    @nameless4630 8 лет назад +6

    This made everything so clear for me! It to totally blew my mind XD I mean I had always memorized the rule but I never actually knew why we have that rule. Thank you so much

  • @vibrane8800
    @vibrane8800 3 года назад

    bro u nailed it mine teacher wasnt able to understand me this concept and in just a video of 2 mins u made me clear like ever u are op

  • @RetroGamingClashOfClans
    @RetroGamingClashOfClans 6 лет назад +5

    and you also should say what pi actually is which is basically how many times the diameter(radius * 2) fits into the circum. and that ratio is pi and the reason pi is infinite is because "a circle is when a line/multiple lines connected reaches infinity", so the ratio can never be one exact number.

    • @misconception9330
      @misconception9330 6 лет назад

      @The Revealer pi actually can not be infinate, only if it's imaginary. Since the angle restriction between 2 each lines will eventually come down to a planck length (1.61622837 × 10^-35 meters).

  • @danielwalker4702
    @danielwalker4702 4 года назад

    The best visual demonstration of the area rule I have ever seen, fantastic!

  • @jmxert6650
    @jmxert6650 Год назад +5

    Ok now the math is mathing..

  • @isabellebedard3097
    @isabellebedard3097 28 дней назад

    Thsi helps so much! I have a test today and I have to explain where the formula comes from! Just one simple question! Why do you cancel out the 2s

  • @jbrittsun
    @jbrittsun 10 лет назад +6

    Can you tell me what software you used to create this video?

  • @arshpreetsingh9295
    @arshpreetsingh9295 3 года назад

    Clear Explaination, Greatly Understood, Perfect Maths, Perfect Learning

  • @hazmatic1673
    @hazmatic1673 4 года назад +3

    my bloody teacher made me watch this

  • @shenniepinote5038
    @shenniepinote5038 3 года назад

    new subscriber here. Your explanation is the best! You make everything so easy.

  • @elixiriskindofpotion1319
    @elixiriskindofpotion1319 10 лет назад +7

    What software are you use for making this video?
    Please reply

  • @MerlinErdogmus
    @MerlinErdogmus Год назад

    Awesome. These animations in correlation with the narration made this whole thing easy and concise to understand. How were these animations Made? Some animations look CPU/GPU intense.

  • @milagonzalez6548
    @milagonzalez6548 9 лет назад +13

    Mind=Blown.

  • @rohinishagarwal9695
    @rohinishagarwal9695 4 года назад +1

    The visuals of this video makes the concept crystal clear! Also, the narrator has explained each concept from its simple to the complex form and also showed how did the formula πr2 came from!

  • @teacherdollie900
    @teacherdollie900 9 лет назад +5

    awesome video, love it! Thank you for making this video.

  • @annettemroskam7450
    @annettemroskam7450 Год назад

    I love this explanation and the visual. Two tweaks would improve it:
    > use different colors for the two halves of the circle (one for top, one for bottom)
    > The twos don't "cancel" out - 2/2 simplifies to 1. This language change is subtle but significant.

  • @carlomikaa
    @carlomikaa 8 лет назад +7

    I learned in a different way

  • @shujin7024
    @shujin7024 4 года назад

    I asked this exact question to a friend and struggled with trying to find a answer for quite a lengthy piece of time. Thanks for the explanation now I know :)

  • @garyesken9746
    @garyesken9746 4 года назад +7

    Pie r square. Everyone knows pie is round

  • @abderrahmanezeglaoui
    @abderrahmanezeglaoui 9 дней назад +1

    that is how these kind of stuff works:
    if you divide this circle infinitely, and get that out and arrange these until it becomes a perfect rectangle!

  • @HANDLEPRINCE
    @HANDLEPRINCE 7 месяцев назад +3

    Legends come here in 2024

  • @RESMITHcarpentry
    @RESMITHcarpentry 2 года назад

    This is the best video of all time for understanding pi and converting square to circle area and vs versa!

  • @hmd-gt
    @hmd-gt 10 лет назад +19

    now i can die in peace ! :D

    • @vicben1
      @vicben1 5 лет назад +2

      but first go ask any or all math & geometry teachers "where does the area of a circle comes from" :D

  • @SenthilKumar-ps3on
    @SenthilKumar-ps3on 5 лет назад +1

    Awesome... Fantastic & Clear explanation..

  • @Abdullah_Osama
    @Abdullah_Osama 5 лет назад +3

    this is Perfect I am goning to Show this video to MY children
    Edit: I will show it to my children when I have them (I am 14)

  • @kindurudineshreddy-jr8uo
    @kindurudineshreddy-jr8uo Год назад

    Excellent explanation Ultimate happiness on watching and knowing

  • @JuhaKona
    @JuhaKona 5 месяцев назад

    every time i watch, i end up smiling and learning something new!

  • @kabulzhan
    @kabulzhan 5 лет назад

    Please answer to this question: at 1:22, why do infinitely cut lines go into each other? If you cut the half circles into infinitely small lines by radius, they should be just lines. Since lines cannot be overlapped, they should be stacked against the lines from the other half circle, not go into each other. Thus, the formula should be: 2 x r x C/2 = 2r x (2rП)/2 = 2r x rП = 2П x r (square)
    Please explain where is the flaw in my logic.

  • @curlylion-animalloverchann6271
    @curlylion-animalloverchann6271 2 года назад +1

    Thanks for explanation, this was awesome!

  • @c.c.1297
    @c.c.1297 3 года назад +1

    Thank you very much for your clear explanation with animation!!! It helped me a lot to fully understand the logic behind the equation. You save me a lot of time figuring it out on my own.

  • @r.a.6459
    @r.a.6459 2 года назад

    Another way is to split the circle into thin concentric rings with width dr. These rings can be regarded as rectangles with area dA. The base of these rectangles are the circumference of the circle, 2πr. (Circumference of the circle is thought to be the first derivative of the area with respect to r)
    Area = Base × Height
    dA = 2πr dr
    ...and then perform the definite integral from r=0 to r=R where R is the radius of the big circle.
    You'll get:
    A = 2πR²/2 = πR²

  • @devenarcher3044
    @devenarcher3044 4 года назад +1

    Thank you so much for this really easy to follow video. I always struggle understanding concepts because I want to know how we derive the formula. This was very helpful!

  • @sean7825
    @sean7825 3 года назад +2

    I think this is a logical fallacy.
    Fallacy: false claim. (I don't know the exact standardized term used but NVM)
    Wouldn't it be a not rectangle?
    1st Claim: Since the prior examples before the infinite division implies that the circle resembles a rectangle but it's not actually rectangle since if we zoom at the edge of the resemblance (the shape), even how large the division of the circle, we can see that it is still not a rectangle.
    1st claim support: The largest division of a circle you can imagine and make it a resemblance of a rectangle will always be the same to the first example of the resemblance in the video if we just zoom at it.
    The thing that I cannot fathom much certainty is the outcome when (the concept of) infinity is applied.
    Of course if the 1st claim is true then even if we apply infinity (concept of) then it will comply to the rule.
    My theory is that it will be an absolute unique shape and its structure is the resemblance, it is not a rectangle but rather a different shape.
    I would love a talk about it.
    P.s. not a mathematician.

  • @apik24
    @apik24 5 лет назад +2

    Thank you so much. Great explanation.

  • @hlalelemahlaela77
    @hlalelemahlaela77 4 года назад

    I'm impressed.
    What a simple but thorough explanation.
    I love your animations.

  • @stephenhare7369
    @stephenhare7369 4 года назад

    First time I’ve ever had it explained as πr times r. Awesome! Thank you for explaining that with visuals - helpful!

  • @sheerahtryphosa65
    @sheerahtryphosa65 3 года назад

    This is EXACTLY what i've been looking for THX sooooooo much!😁🧡

  • @Akuntest-m2c
    @Akuntest-m2c Месяц назад

    I want to ask about your proof so the first question is what it will be look like if all those half of circumstances additio stack that base on the radius will be look like if visuallized

  • @scimastory
    @scimastory 4 года назад +1

    Wow! This is an amazing video. This is so clever -- I never thought of it this way!

  • @japanpanda2179
    @japanpanda2179 9 месяцев назад

    This formula was explained, in a really good way, in the Sir Cumference books which I read as a kid. Amazing books.

  • @LSMaths
    @LSMaths 2 года назад

    Great Sir...Could you please inform us the name of the animation software used?

  • @evertonoliveira7568
    @evertonoliveira7568 2 года назад

    WOOOOOOW, That's so cool, well made and clear!!
    Congratulations!!

  • @youmirinbra458
    @youmirinbra458 3 года назад

    My mind just exploded. First time I actually get why the formula is the way it is, before that I just took it for granted.

  • @johnbrownlolvill
    @johnbrownlolvill Год назад

    This is the best explanation I’ve ever gotten