Find the Area Challenge

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Andy Math

Andy Math

Күн бұрын

Пікірлер: 1 000
@theresamclaird1572
@theresamclaird1572 10 ай бұрын
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 10 ай бұрын
The hard part is to demonstrate that the simples steps lead to the most complex problem (or the other way around)
@dinoaurus1
@dinoaurus1 8 ай бұрын
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 6 ай бұрын
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 4 ай бұрын
if you call this difficult its cos you dont see the smaller steps to begin with
@tttoastbut
@tttoastbut 11 ай бұрын
honestly, the initial problem looks horribly hard. But the solution was actually easy haha. Thanks for the solution :)
@john3260
@john3260 11 ай бұрын
Yeah, the hardest part was figuring out the method to solve it.
@MrBonoxl
@MrBonoxl 11 ай бұрын
You just figured out *everything in life*, congratulations.
@dani.munoz.a23
@dani.munoz.a23 10 ай бұрын
eh, everything seems easy in retrospect
@MrBonoxl
@MrBonoxl 10 ай бұрын
@@dani.munoz.a23 It may be easy, but only when you know how to do it
@anuj68
@anuj68 10 ай бұрын
This video is kinda im sorry to say bullshit because who in their right mind would assume those have to be arcs of circles?
@Metalichap
@Metalichap Ай бұрын
And then the teacher give you a zero because "how can you be sure the curves come from a perfect circle?"
@Idknlandwh123
@Idknlandwh123 19 күн бұрын
and -10 for not writing "cm" even if your country doesn't use cm, and it said nothing about that
@souravde3444
@souravde3444 9 ай бұрын
Usually, students panic on seeing these types of figures and give up. Thanks for simplifying the seemingly complex problem!
@ahmedzanklony8858
@ahmedzanklony8858 6 ай бұрын
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 11 ай бұрын
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 11 ай бұрын
Same, except I’m a rocket scientist
@CertifiedDoc
@CertifiedDoc 11 ай бұрын
@@losthalo428 I find it's always best to just guess when you're making orbital adjustments.
@gummel82
@gummel82 11 ай бұрын
What kind of contractor are you, if you're just estimating?
@0m3gA_o3
@0m3gA_o3 11 ай бұрын
@@gummel82 kinda a pain to count allat
@f2pkx463
@f2pkx463 11 ай бұрын
I don't think it's safe for you to estimate.....​@@losthalo428
@patrickkeller2193
@patrickkeller2193 11 ай бұрын
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 10 ай бұрын
Omg i actually understood this. I was sitting reading this shit for like 5 minutes straight and finally understood it
@yannisconstantinides7767
@yannisconstantinides7767 10 ай бұрын
Was looking for some else that did it by arc segments 👍
@lewqitz
@lewqitz 10 ай бұрын
That's what I did as well.
@magscat493
@magscat493 10 ай бұрын
I simplified it more by drawing the shape in CAD/revit and letting the program do its work. 😭
@logx-ow1us
@logx-ow1us 9 ай бұрын
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.
@jarcuadanantus28
@jarcuadanantus28 10 ай бұрын
Why am I sick and watching math at 9am? I’m almost 30.
@jivvr
@jivvr 4 ай бұрын
it's interesting
@anthraxxru
@anthraxxru 4 ай бұрын
I'm 24 and watching it at 9am as well lol
@ViridRUR10
@ViridRUR10 4 ай бұрын
I swear to god I'm also feeling feverish rn, and it's 12 am😂 High five dude
@astro6040
@astro6040 4 ай бұрын
bro i got a cold rn at 12 am aswell
@mathissofrickinfun
@mathissofrickinfun 3 ай бұрын
Fever sorta, 4,20 AM , but im 15 lol 😂
@gabicerulean
@gabicerulean 10 ай бұрын
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 10 ай бұрын
🤓
@Hunterfury_44
@Hunterfury_44 10 ай бұрын
Blud thinks he's dunny
@Hunterfury_44
@Hunterfury_44 10 ай бұрын
Funny*
@freffrey3772
@freffrey3772 10 ай бұрын
Complexity is nothing but compound simplicity :)
@jomalomal
@jomalomal 10 ай бұрын
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.
@dstarr3
@dstarr3 10 ай бұрын
The shape had me expecting a stealth Silksong announcement
@cobaltcloud64
@cobaltcloud64 7 ай бұрын
shaw!
@andzofficial
@andzofficial 4 ай бұрын
🤡
@peterpan1886
@peterpan1886 10 ай бұрын
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.
@JTCF
@JTCF 10 ай бұрын
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.
@DataScienceDIY
@DataScienceDIY 10 ай бұрын
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 8 ай бұрын
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.
@hkscu
@hkscu 8 ай бұрын
I initially thought thats how he was going to solve it
@DataScienceDIY
@DataScienceDIY 7 ай бұрын
@@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 Ай бұрын
​@@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
@ZantierTasa
@ZantierTasa 11 ай бұрын
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 11 ай бұрын
Life hack 😂
@viliml2763
@viliml2763 11 ай бұрын
this is the best solution
@akultechz2342
@akultechz2342 11 ай бұрын
Easy af
@punpcklbw
@punpcklbw 11 ай бұрын
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 10 ай бұрын
How do you decide on what quarter circles to add and subtract?
@IDE_Busmaster
@IDE_Busmaster 10 ай бұрын
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!
@Xyraphella
@Xyraphella 10 ай бұрын
Silksong when?
@Barsaviak
@Barsaviak 10 ай бұрын
fuck sent my sides to orbit with this
@fleshhammer656
@fleshhammer656 8 ай бұрын
These algebra videos have been great. I learned geometry and such years ago, but forgot the formulas. Nice to have the refresher.
@thanhhai1312
@thanhhai1312 10 ай бұрын
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!
@tagnetorare5401
@tagnetorare5401 10 ай бұрын
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)
@wynnedwards94
@wynnedwards94 11 ай бұрын
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 11 ай бұрын
H
@AjayKumar-mg3xc
@AjayKumar-mg3xc 11 ай бұрын
How would u write equations of the curves tho?
@yuu.kun4
@yuu.kun4 11 ай бұрын
@@AjayKumar-mg3xcthey are circle parts so I think its possible
@wynnedwards94
@wynnedwards94 11 ай бұрын
@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_ 11 ай бұрын
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.
@bitandbob1167
@bitandbob1167 8 ай бұрын
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.
@HenkTheUnicorn
@HenkTheUnicorn 11 ай бұрын
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.
@DuongPham-bd2vr
@DuongPham-bd2vr 3 ай бұрын
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
@cmyk8964
@cmyk8964 11 ай бұрын
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)
@bigbludjosh
@bigbludjosh 7 ай бұрын
Impossible, the Terminids have found their way into our math problems!
@roybixby6135
@roybixby6135 10 ай бұрын
This assumes all curves are spherical - what if they were aspherical ? ...
@jobro8293
@jobro8293 10 ай бұрын
That is the right question to ask.
@LeOwll_
@LeOwll_ 9 ай бұрын
Then it would be impossible to solve thus problem i think
@NFace23
@NFace23 9 ай бұрын
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 9 ай бұрын
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 8 ай бұрын
They do not assume. Read the instructions, it says "made with quarter circles"
@AlvinCwk
@AlvinCwk 11 ай бұрын
Can't believe I am actually sitting in front of this video enjoying math...
@Edarnon_Brodie
@Edarnon_Brodie Ай бұрын
Me seeing a random fugure and trying to create an integral of its function: 🗿
@darkstatehk
@darkstatehk 10 ай бұрын
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!
@ActualDumBatcha
@ActualDumBatcha 11 ай бұрын
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 11 ай бұрын
Exactly my way of thinking and the same solution
@framu3214
@framu3214 10 ай бұрын
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
@dr.downvote
@dr.downvote 2 ай бұрын
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.
@knowhereman7725
@knowhereman7725 11 ай бұрын
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 11 ай бұрын
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 11 ай бұрын
​@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 11 ай бұрын
So true! I swear I have seen very similar comments on other videos like this, that you?
@sohambasak6382
@sohambasak6382 11 ай бұрын
Exactly this!
@user400
@user400 11 ай бұрын
hahaha i envy your minds. how did you even think of splitting it diagonally?
@BlueFireStudiosOfficial
@BlueFireStudiosOfficial 8 ай бұрын
The question looked so hard, but the solution felt like 5th grade. Thanks for this! Subbed.
@balloony3400
@balloony3400 10 ай бұрын
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 10 ай бұрын
by assuming that everything is circles or segments of xd What if they arent?
@Sukkulents_
@Sukkulents_ 10 ай бұрын
@@GaSevilhawell it was stated that every arc was that of a quarter circle…
@TheSpacePlaceYT
@TheSpacePlaceYT 10 ай бұрын
@@Sukkulents_ Bruh I missed that. I would've solved it if I had known.
@GaSevilha
@GaSevilha 10 ай бұрын
yeah, but that makes things too easy doesnt it?@@Sukkulents_
@henryhe5945
@henryhe5945 10 ай бұрын
@@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.
@lichh64
@lichh64 5 ай бұрын
I liked these problems during school because it made me think about something in parts and dissect problems into simpler ones
@davidhowe6905
@davidhowe6905 11 ай бұрын
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.
@cassiuspeter9673
@cassiuspeter9673 Ай бұрын
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.
@headrockbeats
@headrockbeats 11 ай бұрын
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 11 ай бұрын
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
@bahbahbah8460
@bahbahbah8460 10 ай бұрын
thank you for the solution. i'm sure i'll need this to renovate my house with this shape
@dubarnik
@dubarnik 10 ай бұрын
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 8 ай бұрын
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 8 ай бұрын
Who are you man
@samsowden
@samsowden 7 ай бұрын
the problem statement literally says they're quarter circles, so by definition they are.
@tomekk.1889
@tomekk.1889 Ай бұрын
​@@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
@jercki72
@jercki72 4 ай бұрын
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 :)
@cl-cuber6856
@cl-cuber6856 11 ай бұрын
Was able to do it! How exiting!
@Triud45
@Triud45 10 ай бұрын
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.
@francoismusic_
@francoismusic_ 11 ай бұрын
I really love your video, please keep posting video😁
@KengaruZ
@KengaruZ 4 ай бұрын
Man, I wish these videos existed when I went to school
@Amansalwan
@Amansalwan 10 ай бұрын
4:25 game recognise game
@EligibleBubble
@EligibleBubble Ай бұрын
Unironically reteaching me math, something I never thought I’d had to relearn. Thank you
@RafaelMunizYT
@RafaelMunizYT Ай бұрын
silksong geometry
@pewmeowphew
@pewmeowphew 5 ай бұрын
man this is so cool I never thought of this procedure of extracting area
@TheOutcast17
@TheOutcast17 11 ай бұрын
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!
@TrialzGTAS
@TrialzGTAS Ай бұрын
Wish I was stoked on math like this dude
@SnrubSource
@SnrubSource Ай бұрын
Silksong….
@pounchoutz
@pounchoutz 10 ай бұрын
Never thought I'd listen to Anthony jeselnick tutor me in math while I try to sleep
@edocr6833
@edocr6833 11 ай бұрын
yo he got a room upgrade
@StormDiper
@StormDiper 11 ай бұрын
Why am I watching this during winter break?!
@golde727
@golde727 9 ай бұрын
SAME
@tyhatch3771
@tyhatch3771 10 ай бұрын
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 10 ай бұрын
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 8 ай бұрын
"Made with quarter circles" is literally what it says above the square.
@samirstrasser3262
@samirstrasser3262 7 ай бұрын
Uhh, can u read? Lol
@shubhankarbhattacharya1980
@shubhankarbhattacharya1980 7 ай бұрын
Sometimes, less is more.
@lavrentii-kolotushkin
@lavrentii-kolotushkin 4 ай бұрын
How can you be so stupid?
@imnoweren
@imnoweren Ай бұрын
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
@Nightsd01
@Nightsd01 10 ай бұрын
I hated problems like this in school 😂 how do we know those are exact quarter circles
@gu3ee
@gu3ee 8 ай бұрын
very undemocratic looking claw
@haidynwendlandt2479
@haidynwendlandt2479 10 ай бұрын
For those wondering, this area is roughly equal to 36.53 sq units
@lukistar80
@lukistar80 10 ай бұрын
If i didn't check it, i wouldn't know where to search your comment :P Great video tho
@zoommier8220
@zoommier8220 11 ай бұрын
Can't beleive the Nike's logo threw me off so hard from getting a very easy solution, bravo to whoever made this problem
@merchillio
@merchillio 11 ай бұрын
So, if the quarter circles were almost quarter circles but not exactly, we would have been effed? Or maybe with some integrals?
@ethanjsegat
@ethanjsegat 11 ай бұрын
I was thinking the same thing, you wouldn't be able to use the "area of a quarter circle" formula so it might be impossible if the quarter circles were almost quarter circles
@merchillio
@merchillio 11 ай бұрын
@@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 11 ай бұрын
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 11 ай бұрын
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 11 ай бұрын
That’s not what calculus teaches. Go review what a limit is.
@abcbca431
@abcbca431 8 ай бұрын
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
@kamionero
@kamionero 8 ай бұрын
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 2 ай бұрын
Written above drawing: "Made with quarter circles" :)
@johnkuang123
@johnkuang123 Ай бұрын
@@dawidouss6333 What if it isnt a quarter circle, which would make this problem 10x harder to solve.
@dawidouss6333
@dawidouss6333 Ай бұрын
@@johnkuang123 Yes, that would be much harder to solve and I would use integrals to calculate the area.
@johnkuang123
@johnkuang123 Ай бұрын
@@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?
@errisfer
@errisfer 6 ай бұрын
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.
@TheHorseSlayer
@TheHorseSlayer 11 ай бұрын
hey gang, bait used to be believable
@maxtonhughes2629
@maxtonhughes2629 2 ай бұрын
🚬🤡
@Polemimic
@Polemimic Ай бұрын
Y-
@johnryder1713
@johnryder1713 11 ай бұрын
I put a box round this channel and put a value to it, and it certainly will be a high value
@chienliang23
@chienliang23 11 ай бұрын
I am curious about how did you know that each arch is 1/4 circle? Did the question give these premises?
@js7539
@js7539 11 ай бұрын
It says “made with quarter circles” above the diagram
@penepatitenor
@penepatitenor 6 ай бұрын
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
@junj1023
@junj1023 10 ай бұрын
SHAW!
@HEATEDPLA1NS
@HEATEDPLA1NS 22 күн бұрын
WHY CAN I ACTUALLY UNDERTSAND THIS????
@UnizzyMD
@UnizzyMD 10 ай бұрын
mmm… how do we know the curves are perfect circle curvature?
@nachorodriguez6380
@nachorodriguez6380 8 ай бұрын
It says it at the beginning: "Made with quarter circles"
@hildanrachmansyah
@hildanrachmansyah 8 ай бұрын
yea...,yor just dumb didn't literate
@sm_artx
@sm_artx 2 ай бұрын
The math gods are not Greek gods. They cannot be THAT cruel
@nikosucksatskating
@nikosucksatskating Ай бұрын
Because it is defined in the problem.
@ee-ht9rt
@ee-ht9rt Ай бұрын
IT SAYS IT RIGHT THERE
@baxtermullins1842
@baxtermullins1842 10 ай бұрын
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!
@biglargefish4130
@biglargefish4130 11 ай бұрын
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 11 ай бұрын
idk man, i personally think "made with quarter circles" is good enough evidence for me
@superbfacts4786
@superbfacts4786 11 ай бұрын
its given in the ques, just read
@Freelancer.Warzone
@Freelancer.Warzone 11 ай бұрын
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 11 ай бұрын
It’s literally given in the problem that the area is “made with quarter circles”
@cmyk8964
@cmyk8964 11 ай бұрын
What do you think “Made with quarter circles.” means?
@irapramestii
@irapramestii 10 ай бұрын
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!
@faithdriven11
@faithdriven11 10 ай бұрын
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 10 ай бұрын
it is given that they are quarter circles
@garv1204
@garv1204 4 ай бұрын
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
@noelic6744
@noelic6744 11 ай бұрын
I thought it was gonna need some advanced formulas that I don't know, but everything used here was things I learned in 5th or 6th grade. Just used very cleverly. Cool.
@abdullahshah4510
@abdullahshah4510 Ай бұрын
I was searching "how to fall asleep fast" and this no joke came in my reccomend.
@Wesgarbarwil1420
@Wesgarbarwil1420 10 ай бұрын
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
@Grama04
@Grama04 10 ай бұрын
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.
@tiemen9095
@tiemen9095 2 ай бұрын
I cut the bottom-left square diagonally, and flipped the left piece 180° so that the two 2-unit quarter circles coincide. Made for a much easier shape to solve!
@curedbytheonomy
@curedbytheonomy 10 ай бұрын
My homeschooled children are going to love you as their math teacher.
@augustnmonteiro
@augustnmonteiro 5 ай бұрын
I wish youtube would recommend me more content like this!
@epicboss6767
@epicboss6767 10 ай бұрын
What a cool problem! I just found your channel a couple days ago and it is amazing 😁
@xavierrobert3142
@xavierrobert3142 8 ай бұрын
A lazy solution: The figure can be cut in two parts with a SW-NE diagonal. SE side: From the disk segment whose chord is the diagonal of the 12 units square, we remove the disk segment whose chord is the diagonal of the 8 units square. NW side: From the disk segment whose chord is the diagonal of the 8 units square, we remove the disk segment whose chord is the diagonal of the 4 units square. The area is: A = [Area of 1/4 of the circle of radius 12 - Area of the half of 12 units square] - [Area of 1/4 of the circle of radius 8 - Area of the half of 8 units square] + [Area of 1/4 of the circle of radius 8 - Area of the half of 8 units square] - [Area of 1/4 of the circle of radius 4 - Area of the half of 4 units square] We simplify (lines 2 and 3 cancel each other): A = [Area of 1/4 of the circle of radius 12 - Area of the half of 12 units square] - [Area of 1/4 of the circle of radius 4 - Area of the half of 4 units square] That's to say: A = (1/4.π.12² - 1/2.12²) - (1/4.π.4² - 1/2.4²) A = 36.π - 72 - 4.π + 8 A = 32.π - 64
@charlottesphie7037
@charlottesphie7037 29 күн бұрын
Very sharp. I think it is impossible till watching the full video 😂
@ztesch
@ztesch 5 ай бұрын
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!
@jonathanrhodes6180
@jonathanrhodes6180 10 ай бұрын
The real answer is that insufficient information is provided to answer. One must assume right angles and equidistance of the interior line segments. It may seem overly analytical, but real world applications do not tolerate such assumptions and mathematics should not either. For example, if you cut carpet for a "square" room, you may find one side too long and the other too short.
@rusluck6620
@rusluck6620 56 минут бұрын
"Insuffucient information" bro when he learns what a given is: 🤯🤯🤯🤯🤯
@qhc157
@qhc157 10 ай бұрын
The only youtube video makes me get up bed, get a pen and take note at 3AM
@neymarluvr
@neymarluvr 3 ай бұрын
Captain America in another universe where he's a math professor and not an avenger:
@darthtorus9341
@darthtorus9341 5 ай бұрын
The 16π-32 is actually the segment that completes a triangle of the 64-16π. Added together, you get 32 sq units
@wazzzuuupkiwi
@wazzzuuupkiwi 3 ай бұрын
I constructed the red region out of quarter circles minus triangles and got the same answer, how exciting!
@Dead9982
@Dead9982 6 ай бұрын
I didn’t even think that I was really a nerd fr but this video’s actually interesting
@AreolaGrande-y9j
@AreolaGrande-y9j 4 ай бұрын
This is where calculus starts to be the friendlier option
@xzalean
@xzalean 10 ай бұрын
The part that would have stomped me is assuming those arcs were part of a perfect circle or something
@Markus-8Muireg
@Markus-8Muireg 9 ай бұрын
"Made with quarter circles."
@racsofischer7601
@racsofischer7601 10 ай бұрын
An even faster way to solve this, is to rearrange the picture by nestling the little red horn into the curve of the bigger red horn. that way you notice that the shape is actually one big segment with r =3*4=12 minus one small segment with r=4. this gives us a pretty short equation of x=1/4*π(12)^2-1/2*(12)^2-(1/4*π4^2-1/2*4^2)=144π/4-72-16π/4+8=128π/4-64=32π-64 which is the result you ended up with. When there are multiple ways to cut up a shape like this the first step should be to find the best way to describe your area with the least amount of composited shapes in order to avoid doing as much work as possible.
@cocolasticot9027
@cocolasticot9027 4 ай бұрын
Did it in my head, with a simpler decomposition: X is the unknown area, A(r) the area of a quarter disk (=πr²/4) C the area of one cube, You got : X = A(3r) - A(r) - 4C I took r=1 which gives: X = 9π/4 - π/4 - 4 = 2(π - 2) Sawing that the problem gives r=4, multiply the area by the wanted scale (r² = 16): X = 32(π -2) PS : To get to the formula for X I followed the shape from the larger arc then add/remove disks and cubes to fit the shape. Before last simplification, you get : X = A(3) - A(2) - 2C + A(2) - A(1) - C - C
@samuctrebla3221
@samuctrebla3221 10 ай бұрын
There's a most elegant solution of only sums and subtractions of segments of quarter circle if you look at this problem diagonally (literally) Hence only one area formula is necessary, applied to 3 different radii
@mAny_oThERSs
@mAny_oThERSs Ай бұрын
My approach: this minus this plus this minus that plus that minus that plus this and this and minus that plus this and that minus this plus this minus that and that. I was eventually correct after thinking about 20 steps forward into the calculation in my head.
@harivinayak03
@harivinayak03 8 ай бұрын
The solution shows up within the first 10 seconds of the video. Thanks man
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