Find the Area Challenge

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  • Опубликовано: 29 янв 2025

Комментарии • 1,1 тыс.

  • @real-webbe
    @real-webbe Год назад +1899

    I love problems like this because it demonstrates how to take what appears to be a complex/difficult problem, and break it down into simple steps.

    • @loury973
      @loury973 Год назад +14

      The hard part is to demonstrate that the simples steps lead to the most complex problem (or the other way around)

    • @dinoaurus1
      @dinoaurus1 11 месяцев назад +6

      Its crazy watching these as someone who so far only knows middle school math and seeing that I *could* actually figure it out with my current information

    • @nonamehere1626
      @nonamehere1626 8 месяцев назад

      It's why I like to make the distinction between complex and complicated/hard. Most problems are complex, in that they seem daunting but are trivially decomposable like this one. Some problems however are daunting because they are actually hard and can't be decomposed, at least not without great effort. In that case clever simplifications grounded on good assumptions usually go a long way into turning the problem into a complex one.

    • @lifearebennetitwant1007
      @lifearebennetitwant1007 6 месяцев назад

      if you call this difficult its cos you dont see the smaller steps to begin with

  • @tttoastbut
    @tttoastbut Год назад +4176

    honestly, the initial problem looks horribly hard. But the solution was actually easy haha. Thanks for the solution :)

    • @john3260
      @john3260 Год назад +134

      Yeah, the hardest part was figuring out the method to solve it.

    • @MrBonoxl
      @MrBonoxl Год назад +34

      You just figured out *everything in life*, congratulations.

    • @dani.munoz.a23
      @dani.munoz.a23 Год назад +3

      eh, everything seems easy in retrospect

    • @MrBonoxl
      @MrBonoxl Год назад +3

      @@dani.munoz.a23 It may be easy, but only when you know how to do it

    • @anuj68
      @anuj68 Год назад +3

      This video is kinda im sorry to say bullshit because who in their right mind would assume those have to be arcs of circles?

  • @souravde3444
    @souravde3444 Год назад +148

    Usually, students panic on seeing these types of figures and give up.
    Thanks for simplifying the seemingly complex problem!

    • @ahmedzanklony8858
      @ahmedzanklony8858 9 месяцев назад

      I am a student in the second year of secondary school, and I solved this problem correctly, but in a different way, and it took me an hour and 45 minutes of my time.🥲

  • @evilmonkey2184
    @evilmonkey2184 Год назад +3699

    what a crazy solution to a problem like this. as someone who doesn't know the formulas to solve these off the top of my head, i see things like this at work all the time (im a contractor and volume and area come up constantly) and i always just end up estimating. but to be able to crank out a real solution would be so satisfying

    • @losthalo428
      @losthalo428 Год назад +159

      Same, except I’m a rocket scientist

    • @CertifiedDoc
      @CertifiedDoc Год назад +365

      @@losthalo428 I find it's always best to just guess when you're making orbital adjustments.

    • @gummel82
      @gummel82 Год назад +40

      What kind of contractor are you, if you're just estimating?

    • @0m3gA_o3
      @0m3gA_o3 Год назад +14

      @@gummel82 kinda a pain to count allat

    • @f2pkx463
      @f2pkx463 Год назад

      I don't think it's safe for you to estimate.....​@@losthalo428

  • @gabicerulean
    @gabicerulean Год назад +653

    Man, your channel shows exactly what all my math teacher once told me: math is not hard, in fact, it is easy, you just need to decompose the complex processes into simpler ones until you solve everything
    Really nice content, keep on the great work!

    • @Hunterfury_44
      @Hunterfury_44 Год назад +3

      🤓

    • @Hunterfury_44
      @Hunterfury_44 Год назад

      Blud thinks he's dunny

    • @Hunterfury_44
      @Hunterfury_44 Год назад

      Funny*

    • @freffrey3772
      @freffrey3772 Год назад +12

      Complexity is nothing but compound simplicity :)

    • @nakamuii
      @nakamuii Год назад +20

      I get what they meant but that's literally how you accomplish any hard thing; by breaking the problem apart into smaller more manageable problems.

  • @Metalichap
    @Metalichap 4 месяца назад +162

    And then the teacher give you a zero because "how can you be sure the curves come from a perfect circle?"

    • @Idknlandwh123
      @Idknlandwh123 3 месяца назад +19

      and -10 for not writing "cm" even if your country doesn't use cm, and it said nothing about that

    • @Sidowse
      @Sidowse 2 месяца назад +7

      It tells you in the question!

    • @Metalichap
      @Metalichap 2 месяца назад +4

      ​@@Sidowse do you really think I'm that dumb ?
      Cause I am !

    • @hobhamwich77
      @hobhamwich77 28 дней назад

      @@Idknlandwh123 I once got marked down in a physics test because we were asked the basic units of measurement for volume, length, and mass. I said liters, meters, and grams. According to the teacher, the basic unit of measurement in length is cm. What the heck?

    • @BlackOps2543x
      @BlackOps2543x 17 дней назад

      @@hobhamwich77 Well of course in SI the standard unit of length is the meter, but also the standard unit of mass is the kilogram. In CGS, however, the gram is accurate but the meter is not: that of course being the centimeter.

  • @patrickkeller2193
    @patrickkeller2193 Год назад +263

    I did it a bit simpler: cut diagonally the shape is made from two white circle segments cut from two red circle segments. The two radius 8 segments are equal, so we can fit them together and the total area is a radius 12 segment, minus a radius 4 segment, or (36pi-72)-(4pi-8)=32pi-64.

    • @rakhatthenut3815
      @rakhatthenut3815 Год назад +26

      Omg i actually understood this. I was sitting reading this shit for like 5 minutes straight and finally understood it

    • @yannisconstantinides7767
      @yannisconstantinides7767 Год назад +9

      Was looking for some else that did it by arc segments 👍

    • @lewqitz
      @lewqitz Год назад +5

      That's what I did as well.

    • @magsibold
      @magsibold Год назад +4

      I simplified it more by drawing the shape in CAD/revit and letting the program do its work. 😭

    • @logx-ow1us
      @logx-ow1us 11 месяцев назад +4

      You seem pretty good at geometry. I wanted to ask for a few tips. I’m in 7th grade, and I’m taking a geometry class. I’m struggling a lot and so is everyone else. Our last test was somewhat in the middle of difficulty, and it was a derivation of Heron’s formula with no prep, and a few problems from the harder half of AMC10. I just don’t know how I can minimize time wasted. I don’t even erase anymore.

  • @dstarr3
    @dstarr3 Год назад +54

    The shape had me expecting a stealth Silksong announcement

  • @JTCF
    @JTCF Год назад +37

    This is truly beautiful. Like these kinds of problems, you mostly just need to break it up into nice pieces and then it all comes together (pun intended) in such a beautiful way. Love your explanation too.

  • @jarcuadanantus28
    @jarcuadanantus28 Год назад +361

    Why am I sick and watching math at 9am? I’m almost 30.

    • @jivvr
      @jivvr 7 месяцев назад +18

      it's interesting

    • @anthraxxru
      @anthraxxru 7 месяцев назад +5

      I'm 24 and watching it at 9am as well lol

    • @ViridRUR10
      @ViridRUR10 6 месяцев назад +5

      I swear to god I'm also feeling feverish rn, and it's 12 am😂
      High five dude

    • @astro6040
      @astro6040 6 месяцев назад +1

      bro i got a cold rn at 12 am aswell

    • @The_Untitled_Py
      @The_Untitled_Py 6 месяцев назад

      Fever sorta, 4,20 AM , but im 15 lol 😂

  • @thanhhai1312
    @thanhhai1312 Год назад +6

    I watched the other video in the description and I have another solution as well: 1/ calculate the A of the right claw by substracting the larger 1/4 circle (r=12) from the smaller 1/4 circle (r=8) and 2 squares on the left. 2/ calculate the A of the left claw by substracting the larger 1/4 circle (r=8) from the smaller 1/4 circle (r=4) and 1 square in the bottom mid. 3/ Add the A of the 2 claw and substract 1 extra left corner square. This is fun! Thanks for the vid!

  • @crazylegskc
    @crazylegskc Месяц назад +1

    I got it! After I discovered your channel, the first few problems I tried I couldn't get. But I'm getting better and better at them. How exciting!

  • @peterpan1886
    @peterpan1886 Год назад +19

    You can also cut the claw along the diagonal of the bottom left square. Then shift the smaller part to the top right corner of the box and turn it by 180 degrees. Then x is just (1-1/3^2)*A, where A is given by the quarter of the area of a disc with radius 12 minus the area of a square with diagonal 24.

  • @IDE_Busmaster
    @IDE_Busmaster Год назад +23

    What a great video! I had no clue how the process for those inner sections would be calculated when I started and was shocked at how intuitive it was that making them quarter circles and removing the triangle came right as you started saying the solution! Very well structured and paced!

  • @balloony3400
    @balloony3400 Год назад +27

    This is a crazy problem to solve. I thought by clicking on the video I was going to see this being solved with calculus. However, your problem solving solving method stunned me as you were able to make complete sense out such a odd (and complex) question. This is definitely one of the coolest videos I’ve seen lately.

    • @GaSevilha
      @GaSevilha Год назад +2

      by assuming that everything is circles or segments of xd
      What if they arent?

    • @Sukkulents_
      @Sukkulents_ Год назад +5

      @@GaSevilhawell it was stated that every arc was that of a quarter circle…

    • @TheSpacePlaceYT
      @TheSpacePlaceYT Год назад

      @@Sukkulents_ Bruh I missed that. I would've solved it if I had known.

    • @GaSevilha
      @GaSevilha Год назад

      yeah, but that makes things too easy doesnt it?@@Sukkulents_

    • @henryhe5945
      @henryhe5945 Год назад +3

      @@TheSpacePlaceYT That kind of information always has to be given in these kinds of problems. The hardest part of the problem shouldn't be you sitting there wondering if a shape is actually what it looks like. So if you find yourself having to think about that, always go back and check to see if it was already clarified.

  • @fleshhammer656
    @fleshhammer656 10 месяцев назад +1

    These algebra videos have been great. I learned geometry and such years ago, but forgot the formulas. Nice to have the refresher.

  • @ZantierTasa
    @ZantierTasa Год назад +174

    If you add and subtract the obvious quarter circles, and use a pen to keep track of double counting for each little region, you find that you simply overcount by exactly 4 of the squares :)
    Quarter circles: 36pi + 16pi - 16pi - 4pi = 32pi
    Subtract the squares: 32pi - 64

    • @Dinmc123
      @Dinmc123 Год назад +1

      Life hack 😂

    • @viliml2763
      @viliml2763 Год назад +5

      this is the best solution

    • @Necroblade123
      @Necroblade123 Год назад

      Easy af

    • @punpcklbw
      @punpcklbw Год назад +1

      You can also factor out the 16 and radii, seeing that each quarter has a same-size right triangle subtracted, and the r=2 quarters cancel each other out, thus may be omitted.
      Then you simply evaluate 16*(3*3-1*1)*(π/4-1/2) = 128*(π/4-1/2) = 32π-64, which is the correct answer I got just by looking at the figure.

    • @whoisfiel
      @whoisfiel Год назад

      How do you decide on what quarter circles to add and subtract?

  • @bitandbob1167
    @bitandbob1167 10 месяцев назад +2

    Thanks so much for this stepped solution. I struggled with algebra and have not done it for nearly 20 years yet watching this really made my memory trigger with how do all that - i understood it and feel like i could apply those principles in other circumstances.

  • @DataScienceDIY
    @DataScienceDIY Год назад +24

    This problem is extremely easy with some basic calculus. Calculating area by integration is one of the most common problems in early calculus courses. For this problem all you need besides integration is the equation for a circle.

    • @Idran
      @Idran 10 месяцев назад +1

      I mean, that's essentially what he's doing, he's just using the final value of the integral of the equation for a circle from 0 to r, that being pi*r²/4. And I'm not sure this would actually be easier by explicitly defining a bunch of piecewise functions and doing one big integration; that feels like introducing unnecessary complication when you already know the formula for the area under each individual quarter-circle in the grid.

    • @2AitchSquared
      @2AitchSquared 10 месяцев назад +1

      I initially thought thats how he was going to solve it

    • @DataScienceDIY
      @DataScienceDIY 10 месяцев назад +1

      @@Idran They both accomplish the same thing in nearly the same way. Which you find easier probably depends on what you are more familiar with. Fewer fundamental equations are required with calculus, but as you said, more piecewise functions and you need to know how to do basic integration.

    • @tomekk.1889
      @tomekk.1889 3 месяца назад +1

      ​@@DataScienceDIYThis is definitely not as easy as you're describing it. If you'd actually tried to do it with integrals you'd run into trouble. This method is much simpler

  • @BlueFireStudiosOfficial
    @BlueFireStudiosOfficial 10 месяцев назад +2

    The question looked so hard, but the solution felt like 5th grade. Thanks for this! Subbed.

  • @Xyraphella
    @Xyraphella Год назад +28

    Silksong when?

    • @Barasaman
      @Barasaman Год назад +1

      fuck sent my sides to orbit with this

    • @arthurjameson2178
      @arthurjameson2178 Месяц назад +1

      I feel like a conspiracy theorist saying this but I think we find out at the game awards

  • @AlvinCwk
    @AlvinCwk Год назад +2

    Can't believe I am actually sitting in front of this video enjoying math...

  • @tagnetorare5401
    @tagnetorare5401 Год назад +3

    If you cut the area along the diagonal from the top right to the bottom left, and rotate that piece on the left around the center of the large square by 180 degree, you can simply your calculation. The area would be a large circular segment minus a small circular segment, which is 36pi-72-(4pi-8)

  • @Abyss_Enjoyer
    @Abyss_Enjoyer 6 месяцев назад +1

    I used to be afraid of these kinds of problems, until I learned double integrals. Now I can probably solve this in somewhere around 15 mins. Your solution, which only includes basic mathematics, and takes no more than 5 mins, is beautiful

  • @francoismusic_
    @francoismusic_ Год назад +3

    I really love your video, please keep posting video😁

  • @bigbludjosh
    @bigbludjosh 9 месяцев назад +1

    Impossible, the Terminids have found their way into our math problems!

  • @cmyk8964
    @cmyk8964 Год назад +56

    The formula I used involved cutting x down the two bottom left corners. Then if I match the r=8 circle edges together, I get that the area x is:
    (
    a quarter-circle r=12
    minus a triangle b=12 h=12
    ) minus (
    a quarter-circle r=4
    minus a triangle b=4 h=4
    )
    Since it’s trivial that the two parts are similar, I can just simplify it to (3×3 - 1×1) = 8x the hole.
    8 (
    a quarter-circle r=4
    minus a triangle b=4 h=4
    )
    = 8 [ (π×4×4/4) - (4×4/2) ]
    = 8 [ (4π) - (8) ]
    = 32π - 64 (units²)

  • @abcbca431
    @abcbca431 11 месяцев назад +1

    Recently found your channel and i am absolutely in love with your content. As someone who always used to fear math, i recently began on a journey to like math and i cannot tell you how awesome your content has been in guiding me along that journey. As of this peoblem i came close but i coulsnt find out rhe area pf the segment because i didn't visualise it in that way

  • @davidhowe6905
    @davidhowe6905 Год назад +6

    Nice! I managed to do it, similar basic idea of subtracting a group of smaller shapes from a square, but didn't choose such clever ones, hence resorted to using an integral.

  • @penepatitenor
    @penepatitenor 8 месяцев назад

    I dont know why im addicted to watching these. Like, I know the possible ways of figuring it out, but I dont know any of the formulas. Its like watching a friend play a PlayStation game and you know what to do, but you dont know how to handle the controls hahaha

  • @HenkTheUnicorn
    @HenkTheUnicorn Год назад +5

    tl;dr: You can shift the white area above into four white squares and a white quarter circle, turning this problem into something elementary.
    It can be done even quicker and in a much simpler way (even simpler than the trick in the other video). Since you have two congruent quarter circles, a lot of symmetry can be used. Start with the area of the biggest quarter circle π*6^2, the white area outside it is not necessary.
    If you look at the two quarter circles with radius 8 you can actually find two full white squares with them, fit the white area in cell 3 and 6 above the red into the white area above the red in cell 4 and 7. Together with the two cells in the top row you have 4 white squares, so you can subtract 4*4^2 from the total.
    Now the very middle cell is left. In that cell, if you see that the red part in the bottom right has the same area as the white in the top left (again due to symmetry of the two congruent circles) then it suffices to just subtract the area of the smallest quarter circle for the solution.
    So π*6^2-8^2-π*2^2= 32π - 64.
    I think this would be the method with the least amount of calculation.

  • @epicboss6767
    @epicboss6767 Год назад +1

    What a cool problem! I just found your channel a couple days ago and it is amazing 😁

  • @TheOutcast17
    @TheOutcast17 Год назад +7

    im a decade past recalling exact formulas for things like area of a quarter circle or circle segment, so the explicit numbers didn't come to me, but i still got some decent problem solving, worked out the clever shortcut you mentioned from the other guys vid on my own (asking myself "why wouldn't you simplify and do it like this" and felt very vindicated when you pointed to that video and the guy presented the same alternate solution) super neat stuff!

  • @EligibleBubble
    @EligibleBubble 3 месяца назад

    Unironically reteaching me math, something I never thought I’d had to relearn. Thank you

  • @RafaelMunizYT
    @RafaelMunizYT 4 месяца назад +7

    silksong geometry

  • @darkstatehk
    @darkstatehk Год назад +1

    I just love when you see a strange shape in nature, abstract as it may be. Encase it in a symmetrical construction, and calculate the difference. Symmetry, what a wonderful word!

  • @cl-cuber6856
    @cl-cuber6856 Год назад +13

    Was able to do it! How exiting!

  • @Triud45
    @Triud45 Год назад

    I don’t even watch math videos but for some reason this popped up. I watched the whole thing through, super entertaining which I would have never guessed beforehand.

  • @wynnedwards94
    @wynnedwards94 Год назад +30

    Idk why my mind went straight to putting this image on a graph, splitting the curves up into different functions, and finding the area under the curve with integrals and adding them together.

    • @AjayKumar-mg3xc
      @AjayKumar-mg3xc Год назад

      H

    • @AjayKumar-mg3xc
      @AjayKumar-mg3xc Год назад +1

      How would u write equations of the curves tho?

    • @doesntreallymatter0
      @doesntreallymatter0 Год назад +1

      @@AjayKumar-mg3xcthey are circle parts so I think its possible

    • @wynnedwards94
      @wynnedwards94 Год назад

      @AjayKumar-mg3xc Well, it's a 12 by 12 grid that you can put in the first quadrant. You can separate and label each line as a quadratic. For example, that curve that goes from the bottom left corner to the upper right corner can be labeled y=(x^2)/12.

    • @Memories_broken_
      @Memories_broken_ Год назад +1

      I tried to to do this but trust me.. it is NOT easy, you will have to find a lot of intersection points and figure what all areas to subtract. Wouldn't recommend.

  • @irapramestii
    @irapramestii Год назад +1

    Yeayyy got it right on my first try! Your questions remind me of the math olympiads I took part in when I was in elementary school anywayyy. More challenging questions please, I'm so curious!

  • @knowhereman7725
    @knowhereman7725 Год назад +68

    Cool solution, but if you split the shape down the diagonal, you can solve it much easier, because then you can subtract whole quarter circles (plus a small rectangle+triangle shape) from the two larger quarter circles that make up to two arcs we see in the shaded area.

    • @LukesVGArea
      @LukesVGArea Год назад +15

      It gets even better when you see that the two intermediate quarter circles have the same area, so in the end you just need to subtract the tiniest segment of a circle from the biggest one

    • @ConReese
      @ConReese Год назад +15

      ​@LukesVGArea it gets even even better if you print out the problem, cut out the area you're trying to find and then weigh the section and compare it to the total weight of the entire square. You have now calculated area as a measure of weight and then take that ratio and match it against the total area of the shape and itl give you your total area

    • @knowhereman7725
      @knowhereman7725 Год назад

      So true! I swear I have seen very similar comments on other videos like this, that you?

    • @sohambasak6382
      @sohambasak6382 Год назад

      Exactly this!

    • @user400
      @user400 Год назад

      hahaha i envy your minds. how did you even think of splitting it diagonally?

  • @jercki72
    @jercki72 7 месяцев назад

    Props for mentioning the MYD video! How exciting indeed. For me the part I didn't figure out was to cut the top right square in half :)

  • @roybixby6135
    @roybixby6135 Год назад +282

    This assumes all curves are spherical - what if they were aspherical ? ...

    • @jobro8293
      @jobro8293 Год назад +46

      That is the right question to ask.

    • @LeOwll_
      @LeOwll_ 11 месяцев назад +59

      Then it would be impossible to solve thus problem
      i think

    • @NFace23
      @NFace23 11 месяцев назад +47

      the curves must be circular if they have constant curvature and intersect the squares at exactly their vertices. Neither of which is specified in the problem. So you're right it's a poorly conditioned problem.

    • @CertifiedDoc
      @CertifiedDoc 11 месяцев назад +13

      Then you estimate and get as close as is reasonable.
      Or, you use calculus. You measure the rate of curvature for each section of the curve, represent that with a function, and integrate over the range.

    • @kryum
      @kryum 11 месяцев назад +102

      They do not assume. Read the instructions, it says "made with quarter circles"

  • @Edarnon_Brodie
    @Edarnon_Brodie 4 месяца назад +3

    Me seeing a random fugure and trying to create an integral of its function: 🗿

  • @pounchoutz
    @pounchoutz Год назад

    Never thought I'd listen to Anthony jeselnick tutor me in math while I try to sleep

  • @ActualDumBatcha
    @ActualDumBatcha Год назад +11

    This is a pretty complex solution. I just thought of moving the smaller offcut by translation and rotation inside the big offcut, making it a segment - a smaller segment. in the end you get smth like (36π - 72) - (4π - 8) getting 32π - 64. How, exciting.

    • @stanchern3796
      @stanchern3796 Год назад

      Exactly my way of thinking and the same solution

    • @framu3214
      @framu3214 Год назад

      Or just calculate the big one and multiply by 8/9 since you know that the smaller one is 1/3 in lenght so is 1/9 in area

  • @bahbahbah8460
    @bahbahbah8460 Год назад +1

    thank you for the solution. i'm sure i'll need this to renovate my house with this shape

  • @headrockbeats
    @headrockbeats Год назад +7

    I went by a different route (also I used X for the length instead of 4). I cut the red shape along the diagonal, which meant:
    Large Shape area
    = Quarter circle of 3X radius - Quarter circle of 2X radius - 2 squares of length X - 1/2 squares of length X
    = (Pi*(3X)^2)/4 - (Pi*(2X)^2)/4 - 2(X^2) - (X^2)/2
    Small Shape area
    = Quarter circle of 2X radius - Quarter circle of X radius - square of length X - 1/2 squares of length X
    = (Pi*(2X)^2)/4 - (Pi*X^2)/4 - (X^2) - (X^2)/2
    Add the two together:
    Total_area = (Pi*(3X)^2)/4 - (Pi*(2X)^2)/4 - 2(X^2) - (X^2)/2 + (Pi*(2X)^2)/4 - (Pi*X^2)/4 - (X^2) - (X^2)/2
    Multiply everything by 4 to get rid of the divisors:
    4 * Total_area = Pi*(3X)^2 - Pi*(2X)^2 - 8(X^2) - 2(X^2) + Pi*(2X)^2 - Pi(X^2) - 4(X^2) - 2(X^2)
    Open the squared parentheses
    4 * Total_area = 9Pi(X^2) - 4Pi(X^2) - 8(X^2) - 2(X^2) + 4Pi(X^2) - Pi(X^2) - 4(X^2) - 2(X^2)
    Add up
    4 * Total_area = 8Pi(X^2) - 16(X^2)
    4 * Total_area = (8Pi-16) X^2 sq. units
    Divide both sides by 4
    Total_area = (2Pi-4) X^2 sq. units
    Same solution, just plug in whatever value you want for X.

    • @yaroslavpanych2067
      @yaroslavpanych2067 Год назад

      I agree, having to calculate only 4 areas (of the same shape) is much faster (and better) solution. Saving x as symbol to plug it in later is cherry on top

  • @johnryder1713
    @johnryder1713 Год назад

    I put a box round this channel and put a value to it, and it certainly will be a high value

  • @kamionero
    @kamionero 11 месяцев назад +21

    1:33 How do you know the arcs are a quarter circle? Thats an assumption that the drawing doesnt really confirm. It could be a slightly asymptotic line, not a radial.

    • @dawidouss6333
      @dawidouss6333 5 месяцев назад +26

      Written above drawing: "Made with quarter circles" :)

    • @johnkuang123
      @johnkuang123 3 месяца назад

      @@dawidouss6333 What if it isnt a quarter circle, which would make this problem 10x harder to solve.

    • @dawidouss6333
      @dawidouss6333 3 месяца назад +2

      @@johnkuang123 Yes, that would be much harder to solve and I would use integrals to calculate the area.

    • @johnkuang123
      @johnkuang123 3 месяца назад

      @@dawidouss6333 What if its a hand drawn shape that's all over the place? random curves like a blob of slime, is it even possible to find the area?

  • @dr.downvote
    @dr.downvote 5 месяцев назад +1

    Kids, this is exactly what most of the maths is all about. It’s not about remembering the formula for area of cylinder or a scalene triangle, it’s about how do you approach a solution given the formulae. Anyone who doubts their education system should watch this.

  • @Nightsd01
    @Nightsd01 Год назад +4

    I hated problems like this in school 😂 how do we know those are exact quarter circles

  • @lichh64
    @lichh64 7 месяцев назад

    I liked these problems during school because it made me think about something in parts and dissect problems into simpler ones

  • @Amansalwan
    @Amansalwan Год назад +42

    4:25 game recognise game

  • @zoommier8220
    @zoommier8220 Год назад

    Can't beleive the Nike's logo threw me off so hard from getting a very easy solution, bravo to whoever made this problem

  • @edocr6833
    @edocr6833 Год назад +3

    yo he got a room upgrade

  • @BUETisAim
    @BUETisAim 7 месяцев назад

    man this is so cool
    I never thought of this procedure of extracting area

  • @dubarnik
    @dubarnik Год назад +17

    The assumption that the two areas are segments of a circle could be wrong. He's assuming by inspection that the curves have an eccentricity of zero and are, hence, part of the circumference of circles, but this might not be the case. Other types of curves can also connect the two endpoints. So, interesting solution but based on what could be two faulty assumptions.

    • @MicaelAlighieri
      @MicaelAlighieri 10 месяцев назад

      It clearly isn't the case, at least for me, so his calculations are wrong, the outer parts of the circumferences reach the edges too early.

    • @sanjuali3096
      @sanjuali3096 10 месяцев назад +1

      Who are you man

    • @samsowden
      @samsowden 10 месяцев назад +6

      the problem statement literally says they're quarter circles, so by definition they are.

    • @tomekk.1889
      @tomekk.1889 3 месяца назад

      ​@@samsowdenJudging by how many people didn't notice it it probably should have been stated out loud at the beginning of the video. He's simplofying the problems too much for younger viewers and missing the nuance

  • @huh5950
    @huh5950 Год назад +1

    The only ptoblem I had is I didnt knoe how to get the area of the 2 slices, nice, thank you for the explanation

  • @haidynwendlandt2479
    @haidynwendlandt2479 Год назад +4

    For those wondering, this area is roughly equal to 36.53 sq units

    • @lukistar80
      @lukistar80 Год назад +1

      If i didn't check it, i wouldn't know where to search your comment :P Great video tho

  • @KengaruZ
    @KengaruZ 7 месяцев назад

    Man, I wish these videos existed when I went to school

  • @merchillio
    @merchillio Год назад +6

    So, if the quarter circles were almost quarter circles but not exactly, we would have been effed? Or maybe with some integrals?

    • @merchillio
      @merchillio Год назад +6

      @ethanjsegatI watched the other video mentioned and the shape is made using explicitly mentioned quarter circles so there’s no assumption, but if I was just given the shape like that, I wouldn’t be comfortable just assuming they’re quarter circles

    • @noahbradley4146
      @noahbradley4146 Год назад +1

      If they weren't exactly quarter circles then yeah we'd be effed. Unless they gave enough information that you could work out the function of the curve in which case I think integrating to find the area under the curve would be correct.

    • @leekyonion
      @leekyonion Год назад +2

      Good thing is that in real life, you can estimate and be within a margin of error. We're conditioned so early on that math has to have one singular answer but Calculus teaches you that there are multiple approaches and that you can always be within an error of margin. Dividing a line into infinitely many pieces to guess where it most likely converges is peak guessing game and I love it

    • @katolson8802
      @katolson8802 Год назад +1

      That’s not what calculus teaches. Go review what a limit is.

  • @qhc157
    @qhc157 Год назад

    The only youtube video makes me get up bed, get a pen and take note at 3AM

  • @UnizzyMD
    @UnizzyMD Год назад +323

    mmm… how do we know the curves are perfect circle curvature?

    • @nachorodriguez6380
      @nachorodriguez6380 11 месяцев назад +166

      It says it at the beginning: "Made with quarter circles"

    • @hildanrachmansyah
      @hildanrachmansyah 10 месяцев назад

      yea...,yor just dumb didn't literate

    • @sm_artx
      @sm_artx 4 месяца назад +29

      The math gods are not Greek gods. They cannot be THAT cruel

    • @nikosucksatskating
      @nikosucksatskating 4 месяца назад

      Because it is defined in the problem.

    • @ee-ht9rt
      @ee-ht9rt 3 месяца назад +16

      IT SAYS IT RIGHT THERE

  • @StormDiper
    @StormDiper Год назад +1

    Why am I watching this during winter break?!

  • @SnrubSource
    @SnrubSource 4 месяца назад +7

    Silksong….

  • @baxtermullins1842
    @baxtermullins1842 Год назад

    A polar planimeter! I have a K&E device - of course I bought mine in 1967 as an engineering student. But, today there are some interesting computer programs to integrate the thing! Love the computer!

  • @tnsquidd
    @tnsquidd 4 месяца назад +3

    What so silksong does to a man

  • @garv1204
    @garv1204 6 месяцев назад

    I did these type of questions as a cakewalk at 12 year age before COVID
    But now I forget all I start fearing from them
    Seeing your approach towards ques reminds me of my prime

  • @gylastra3163
    @gylastra3163 5 месяцев назад +3

    Shaw?

  • @harivinayak03
    @harivinayak03 11 месяцев назад

    The solution shows up within the first 10 seconds of the video. Thanks man

  • @junj1023
    @junj1023 Год назад +3

    SHAW!

  • @TrialzGTAS
    @TrialzGTAS 4 месяца назад

    Wish I was stoked on math like this dude

  • @tyhatch3771
    @tyhatch3771 Год назад +140

    I’m mad AF, because there’s no part of the problem telling us that the curve is a quarter circle! Yes, it touches the two corners, but there nothing telling us that each point along its curve is equidistant from its center point. It’s spent a good ten minutes trying to figure out the curvature of the shape.

    • @sibonelodlamini6782
      @sibonelodlamini6782 Год назад +6

      You can assume that the radius of the circle is 8... and that's how he knows that it's a quarter circle. It's will help you calculate the area within that region

    • @infinnity2351
      @infinnity2351 10 месяцев назад +105

      "Made with quarter circles" is literally what it says above the square.

    • @samirstrasser3262
      @samirstrasser3262 10 месяцев назад +7

      Uhh, can u read? Lol

    • @shubhankarbhattacharya1980
      @shubhankarbhattacharya1980 10 месяцев назад

      Sometimes, less is more.

    • @lavrentii-kolotushkin
      @lavrentii-kolotushkin 7 месяцев назад

      How can you be so stupid?

  • @Wesgarbarwil1420
    @Wesgarbarwil1420 Год назад

    I am obsessed with this sort of stuff. I knew all of those equations but I just did not see the broken down shapes. This is soooo easy once you break it down

  • @chienliang23
    @chienliang23 Год назад +12

    I am curious about how did you know that each arch is 1/4 circle? Did the question give these premises?

    • @js7539
      @js7539 Год назад +17

      It says “made with quarter circles” above the diagram

  • @Warbalz
    @Warbalz Год назад

    And here i am, randomly getting this video on my feed, looking more dam stupid. Even though i used to go to maths faculty in high school, i feel i know nothing but the basics.. also never have thought maths could be this interesting. great channel fam, best wishes to you!

  • @TheHorseSlayer
    @TheHorseSlayer Год назад +18

    hey gang, bait used to be believable

  • @xzalean
    @xzalean Год назад

    The part that would have stomped me is assuming those arcs were part of a perfect circle or something

  • @alvagant7444
    @alvagant7444 Год назад +3

    bait used to be believable

  • @curedbytheonomy
    @curedbytheonomy Год назад

    My homeschooled children are going to love you as their math teacher.

  • @biglargefish4130
    @biglargefish4130 Год назад +6

    My only issue is that by default you assume the curves are circular if that werent the case itd probably be unsolvable. Either way very impressive its a neat seeing you solve these

    • @ActualDumBatcha
      @ActualDumBatcha Год назад

      idk man, i personally think "made with quarter circles" is good enough evidence for me

    • @superbfacts4786
      @superbfacts4786 Год назад +5

      its given in the ques, just read

    • @Freelancer.Warzone
      @Freelancer.Warzone Год назад +2

      if it was unsolvable on purpose, then what would be the point of it?
      from where I see it, this problem tries to teach you how to approach a problem, and how much easier it is when you consider other alternatives.
      when the entire point of problems and whatnot is to TEACH, then there is no reason for it to be unsolvable

    • @taberbooth9203
      @taberbooth9203 Год назад +5

      It’s literally given in the problem that the area is “made with quarter circles”

    • @cmyk8964
      @cmyk8964 Год назад +3

      What do you think “Made with quarter circles.” means?

  • @imnoweren
    @imnoweren 4 месяца назад

    this is why, i always think that half of math is knowledge and the other half is creativity, and creativity can be improved through practice

  • @faithdriven11
    @faithdriven11 Год назад +4

    You’re making a few assumptions here without having any evidence to support your assumptions, such as those circles, being quarter circles, and the value that they take up.

    • @jonprice5522
      @jonprice5522 Год назад +5

      it is given that they are quarter circles

  • @mr.donut2.085
    @mr.donut2.085 10 месяцев назад +1

    I got the same result but with a different way of calculating. I calculated the area of the big quarter circle and subtracted the triangle part and the round part of the smaller quarter circle and so on.

  • @ztesch
    @ztesch 8 месяцев назад

    I find that for shapes like this, it's usually just easier to write the curves as semicricle equations (y = sqrt(radius^2 - x^2)) and then use integrals to find the volumes of solids. however, the way that you did it is super cool!

  • @charlottesphie7037
    @charlottesphie7037 3 месяца назад

    Very sharp. I think it is impossible till watching the full video 😂

  • @augustnmonteiro
    @augustnmonteiro 8 месяцев назад

    I wish youtube would recommend me more content like this!

  • @Grama04
    @Grama04 Год назад

    not the shortest or simplest way to solve this problem but as a teacher myself I know what you are doing here and Ike it. well done.

  • @Dead9982
    @Dead9982 8 месяцев назад

    I didn’t even think that I was really a nerd fr but this video’s actually interesting

  • @lolcestlol4619
    @lolcestlol4619 9 месяцев назад

    yoooo that's insane! keep up the good work dude !

  • @gu3ee
    @gu3ee 11 месяцев назад +2

    very undemocratic looking claw

  • @cassiuspeter9673
    @cassiuspeter9673 4 месяца назад +1

    It's funny how much the "made with quarter circles" knocks the difficulty of this problem way down.
    Funnily enough, I did it a completely different way: I started with the full square, and imagined either cutting the square off or adding to it, keeping track of what was added/subtracted. I got to the correct answer, and I only needed to use the formulas for circles and squares, but I get the feeling my idea was a tad more complex than this. Definently more error-prone.

  • @wazzzuuupkiwi
    @wazzzuuupkiwi 5 месяцев назад

    I constructed the red region out of quarter circles minus triangles and got the same answer, how exciting!

  • @abdullahshah4510
    @abdullahshah4510 4 месяца назад

    I was searching "how to fall asleep fast" and this no joke came in my reccomend.

  • @BattleFranky666
    @BattleFranky666 Год назад

    This man is a menace, Great video

  • @TaeKinzel
    @TaeKinzel Год назад

    I watched some of your videos and thought “Why didn’t I think of that?” and the next video you make I will actually think about it and try.

  • @masonscasualaccount2726
    @masonscasualaccount2726 Год назад +1

    Finding the quarter circles and unknown shapes are the regions I still have no idea how to get. Because I would never know how to get those from a square, not knowing exactly how much of the square it takes up.

    • @bardsamok9221
      @bardsamok9221 Год назад

      The quarter circles all intersect on the grid giving exact dimensions of the circles :) Just count the grid and get their area. Try it on paper one step at a time :) You'll get it.
      I just started with the obvious shapes and what you can do with the different sized triangles and squares from the grid intersections. Then link the numbers at the end and simplify the equations if you like.
      Remember the squares of different sizes can be divided into 2 diagonally to get triangles when you need a segment.
      Subtract a triangle from a quarter circle to get the remaining part (the segment).
      Subtract shapes from shapes.
      Helps to use paper so you can keep the sections separate. Maybe different colour pen for the different parts would help order on your page before simplifying. Practice rearranging equations.
      Tip: You might find it easiest to remove the white areas from the total area of the square to be left with the red area (x)

  • @errisfer
    @errisfer 8 месяцев назад +2

    1:11 I think these are called spandrels. At least that's what we called them when dealing with the centroid and the rational inertia about these shapes.

  • @ALiBi212x
    @ALiBi212x Год назад

    bro I love this channel