The first comment is from 1 month ago because I posted it to Math StackExchange where I received great help: math.stackexchange.com/questions/3016718/a-way-to-find-this-area-without-calculus Early comments also come from Patreon, as I do my best to give early access to supporters on Patreon: www.patreon.com/mindyourdecisions And finally, thanks for 1 million subscribers! We are building one of the best mathematical communities in the world. Thank you.
@jonbell35315 жыл бұрын
Hi Mind your decisions, isn't the solution just a specially sheared version of a slice of the upper semicircle limited by points P and Q?
@matheusmendes49695 жыл бұрын
Hey, I solved it in a different way that does not require as much knowledge of trigonometry!
@canaDavid15 жыл бұрын
Now noone has an excuse for saying "first"
@Doppio55 жыл бұрын
Hi mind your decisions I have a problem for you: In a trapeze abcd (ab||dc) The ac and bd diagrams are cut at point e the ratio between the bases is 4:9 and the area of the triangular bec is 108 What is the area of the whole trapeze?
@juanperezmondragon16765 жыл бұрын
Matheus Mendes yeah I also did it , well I used basic geometry and one equation system.
@rayvon28065 жыл бұрын
Just check the resolution of picture and count the red pixels. It will be surprisingly accurate.
@onnilattu91385 жыл бұрын
Yeah this is big brain time.
@sayantan22015 жыл бұрын
That is actually a legit answer. The method is Monte Carlo method.
@technosiam44805 жыл бұрын
Tell me this Sfhnxdkmvddghcssasfhkkmnjggcghjhy cnbvyul iyvvjygvbjuydfvjjnnb hgjjbffhjgtynoolmnbc hhyrszxvnklopplkkjhgh
@Deibler6664 жыл бұрын
That is the basis for calculus.
@DrTWG4 жыл бұрын
@@technosiam4480 I see what you mean.
@slvtlv86965 жыл бұрын
Another solution: print it on a paper, cut out the red part, weight it, divide by the total weight.
@adrianpaweek32984 жыл бұрын
this may sound funny but it's how they did it before calculus/geometry was common, in fact no so long ago, math became more common in 18th century or so
@wifebeater694 жыл бұрын
@ then print a modified picture of it without the red part colored in
@mohammedarjunaid14954 жыл бұрын
Lame
@adrianpaweek32984 жыл бұрын
@Aryan Sharma you think from perspective of today. Note that only few in only few nations knew this in ancient times. Rest of nation was not able to read or write. What more geometry was expressed primarily graphically, there wasn't kind of todays' equations.
@sextupledvanillabeans5594 жыл бұрын
Engineers vs mathematicians
@PhoenixLive_YT3 жыл бұрын
-"the first method is simple" me: "alright, this might be the first time where i can solve a hard Math problem on my ow..." -"shows space rocket schematic" me: "okay, next video"
@schwartzseymour3573 жыл бұрын
I'm just watching it to see what I DON'T understand.
@janjan555553 жыл бұрын
@@schwartzseymour357 Just watch the first method, the other ones are waaaay too abstract and you're needlessly complicating things. With some knowledge of geometry and testing your 3D logical insight it's fairly doable. If you lack these concepts, yeah this video is as good as impossible for any newbie.
@williamhexberg67483 жыл бұрын
@@janjan55555 I disagree. If you know integral calculus, the third method is VERY straight forward, and is definitely the way I would have went before he even mentioned the geometric solutions.
@janjan555553 жыл бұрын
@@williamhexberg6748 I do and I still disagree with your method
@jerryliu61503 жыл бұрын
@@janjan55555 To me the integral method feels brute force and it’s the way I went about solving it before watching the explanation. I was expecting some clever/creative geometry trick and it turned out to be really simple. I just couldn’t see it.
@AntonOrSomething3 жыл бұрын
I'm proud of myself for this one. It is the first time I solved one of your math puzzles. It took me like an hour but I got the right result of 9.77 I'm only 14 years old and I've never had anything like this in school before.
@Soefae2 жыл бұрын
Ayo good job!!
@AntonOrSomething2 жыл бұрын
@@Soefae lol, you answer on my 11 month old comment. But anyways, thank you
@commonlogicart16042 жыл бұрын
@@AntonOrSomething out of curiosity, if you didn’t learn it in school then where did you learn it? And which method did you use?
@AntonOrSomething2 жыл бұрын
@@commonlogicart1604 I found some method to calculating the different circle pieces area, and subtracting them. But it's almost a year ago, so I don't remember exactly what I did.
@tomomi12 жыл бұрын
I'm 14 too and I get 21.4
@mamertvonn4 жыл бұрын
you know i've been watching a couple of your vids and there's usually a common theme in finding the correct answer. Either you use coordinates or geometry. When using geometry there's always one rule... find triangle and you'll find the answer. Just throwing that out. It's amazing to how much extent you can use this simple concepts to solve something like this
@mathpedia13 жыл бұрын
Solve this problem guys. This is a challenge for you. Problem given in the link below. kzfaq.info/get/bejne/ps2Hq5p0ztaqnKM.html
@cdmcfall2 жыл бұрын
Yup. This is exactly why trigonometry is taught as a standalone course and not as the subset of geometry that it is.
@AhmedHan5 жыл бұрын
Next video: Put many circles inside a square; make most of them pass from intersections of other circles. Find the most absurd looking piece of area. And then solve for it.
@Kyle-ns4yk5 жыл бұрын
@Tokisaki Kurumi using only a ouija board
@massimookissed10235 жыл бұрын
And then realise a 7 year old Korean kid solved it quicker than you did.
@pkmelodies34265 жыл бұрын
U don't have any other work or what?🤔😑
@karljo80644 жыл бұрын
haha, this one is so complicated i don't want to watch through it.
@sayoriutsugj28564 жыл бұрын
AhmedHan that actually sounds fun
@vk42892 жыл бұрын
For those who are wondering where π came for θ, it is the radian system or circular system for angles. 180 degree = π radian. And 1 radian = 57 degree (approx). *And 1 radian can also be represented by the angle formed at the centre of a circle by 2 radii separated by an arc of 1 unit length (on the circumference of the circle)*
@Mike-rw1jw Жыл бұрын
this is a 7th grade problem
@pleasedontlookforme8036 Жыл бұрын
@@Mike-rw1jw akshully I could do it at 1st grade 🤡
@askanddevanand46513 жыл бұрын
Any mathematics enthusiast will be blessed by finding this channel...Hats off to the creator❤️🎉🙏👍
@outernetisdangerous5 жыл бұрын
I’m majoring in Mechanical Engineering and the calculus method seemed to be the easiest method. 😂
@KingBobXVI4 жыл бұрын
It included the most important step I remember from my calculus class - "annnd... skip some steps". Though in my class this was the "and from there... it's obvious" step :P
@MAKChaosLander4 жыл бұрын
I dont think so, its easier to error with calculus, and more work demanding in my opnion. If you can work with basic algebra or geometry and have a good trig perception you should use it. Calculus is too powerfull, like trying to catch a fly with a gun when you have a fly swatter.
@theunique1404 жыл бұрын
1! +2!+ 3! +...........25! divided by 13 then what will be the remainder left?
@jjm77974 жыл бұрын
@@theunique140 Using python. x = 0 for i in range(1,26): x += factorial(i) x%13 = 9
@goudaeater51073 жыл бұрын
@@theunique140 If you're still looking for an answer, you can do it like that 1! + 2! + 3! + ... + 12! + 0 (x!%13 = 0 for x>=13) 1(1 + 2(1 + 3(1 + 4(1+5(1+6(1+7(1+8(1+9(1+10(1+11(1+12))))))))))) % 13 11*(12+1) = 11*0 10*1 9*11 = 99, 99%13 = 8 8*9 = 72, 72%13 = 7 7*8 = 56, 56%13 = 4 6*5 = 30, 30%13 = 4 5*5 = 25, 25%13 = 12 4*0 = 0 3*1 = 3 2*4 = 8 1*9 = 9
@bhcf2m3 жыл бұрын
I paused the video and solved the problem on my own before watching the full video. I approached it geometrically. I did it in my head without even using paper and pencil. I thought it was quite simple. I continued to watched the full video just to make sure I got the same answer. I was surprised that all the 3 methods in the videos are so long. Below is the outline of my method. Using the same labelling as 00:34 of the video, Area of shape DPQ = Area of shape DPQC - Area of shape DQC. It is easy to see that the shape DPQC repeated 4 time will fill the square. So the area of DPQC is just 25. Next step is to solve for area of shape DQC. Let midpoint of DC be E. Area of DQC = Area of sector QEC + Area of quadrilateral DEQA - Area of sector DAQ. It can be easily checked that Angle QEC = 2 * Angle QDC = Angle QAD = 2 * tan^-1(0.5). Therefore, Area of shape DQC = pi * 5^2 * (2 * tan^-1(0.5)/2pi) + 2 * 1/2 * 5 * 10 - pi * 10^2 * (2 * tan^-1(0.5)/2pi) =50 - 75*tan^-1(0.5) Finally, Area of DPQ = Area of shape DPQC - Area of shape DQC = 25 - (50 - 75*tan^-1(0.5)) = 75*tan^-1(0.5) -25 This is the same answer. I didn't finish reading all the 1.5k comments. But so far among the comments I've read, I haven't seen a similar method. This is the first time I see this problem. I'm not sure whether or not this method above has been posted before elsewhere on the internet.
@GGReaver2 жыл бұрын
Finally an elegant solution without huge calculations and variables. Bravo!
@bhcf2m2 жыл бұрын
@@GGReaver Thanks for taking notice of my solution. I thought no-one would bother reading it 😆
@pain67974 жыл бұрын
Me: I know calculus well Me after watching this: I know nothing about calculus
@kaos70123 жыл бұрын
Facts. I haven't even begun learning integral calculus, only differential, so I found the geometry a million times easier to understand.
@DanTheManTerritorial3 жыл бұрын
This was basic calculus actually, you do have some problems
@kameronrogers40003 жыл бұрын
@@DanTheManTerritorial lmao, you have the reduction formulas memorized?
@kameronrogers40003 жыл бұрын
Don't feel bad, unfortunately this problem calculus wise is very reliant on formulas from table of integrals. The solving was largely done by the reduction formulas, which I don't think any reasonable calc teacher would expect u to have memorized because they don't pop up that often, outside of situations like this where the curves happen to be parts of circles.
@pankajdas1423 жыл бұрын
@@kameronrogers4000 no it would if you have enough practice of indefinite integration during 12th std, or even if you face such difficulty later you could always look on internet, these are basic reduction
@halfmoon265 жыл бұрын
i have enough problems in my life
@pkmelodies34265 жыл бұрын
😂😂😂😂😂😂😂
@windragon3795 жыл бұрын
This stuff is precisely to distract you from problems in life. XD
@rawlingselom59164 жыл бұрын
😂😂😂😂... Swears
@shondellcelestine33154 жыл бұрын
LMAO relatable😂😂😂
@soumyaranjankanr3064 жыл бұрын
Maths book: "Cute"
@bennyfactr61225 жыл бұрын
If I only had 5min to solve, I would answer "definitely less than 100" & walk away
@natepolidoro45655 жыл бұрын
exactly
@hendrilibrata33535 жыл бұрын
"definitely less than 50" to be more accurate
@eggyrepublic5 жыл бұрын
@TheMutedGamer I would bet it was less than 18. (haven't watched yet)
@idmarilamri63985 жыл бұрын
Well definetely more than zero
@danpat81355 жыл бұрын
@Yash Hriddha I bet it's 9.77
@shiladityachakraborty63732 жыл бұрын
As an alternative, one might use symmetry and scale to simplify the solution. Steps: 1) 'Symmetrize' the picture by drawing another quarter circle radius 10, centered at the TOP, RIGHT vertex of the square. This divides the square into 8 regions, of which 3 are pairwise identical, thereby resulting in 5 distinct shapes ( with areas x1 thru x5). Our target region (shown in red in video) is one of the paired regions (say x2). 2) Express the areas of the small semicircle, the large quarter circle, and the square as linear equations in the variables x1 thru x5. 3) Thus far we have 3 linear equations, (and 5 unknowns) so we need 2 more. These are a) The area of the small 'lens' region formed by the intersection of the two semicircles, which can be easily computed as described in the video, or otherwise. and b) The area of the larger 'lens' formed by the intersection of the two large quarter circle. Since the larger lens has the same shape and twice the linear dimensions as the smaller lens, its area is 4 times as large. 4) Now we have a complete set of equations, from which x2 can be easily obtained.
@christophmayer39912 жыл бұрын
Thought that would be the "best" solution as well when trying the problem on my own, but sadly the equation system is underdetermined and you can't solve for x2 (the red "wanted" region) with these equations alone. You somehow need to calculate the area of one of the "paired" regions on their own and for that you always need the right most corner of the red region (or its symmetrical counterpart). And at that point you can just use the calculus solution from the get go...
@geminwanzo4 жыл бұрын
9:00 instead of using trig functions, we can also apply the similar triangles rule. Find the ratio of the kite triangle and smaller triangle hypotenuse, then their areas have ratio to the square
@fc634575 жыл бұрын
Option 4 - Depending on how many sig figs you need. Step 1: Find a sheet of graphing paper. Step 2: Sse a compass and rulers to draw out the figure. Step 3: Spend the last 3 hours of the exam to count the number of little squares.
@sykes10244 жыл бұрын
This is essentially how some computer programs compute areas. They just make the squares small enough so that they get the desired precision and of course they can count the squares much faster :)
@user-mx4sx1ul8h4 жыл бұрын
마인드 유어 디시젼
@swipingeverymoment3 жыл бұрын
@@user-mx4sx1ul8h dak chua!!
@AlexanderGieg3 жыл бұрын
I work at a railway testing lab. There's a test that involves pressing a rubber pad in between a mechanical actuator and a cast iron mold with small high relief squares carved on it, over which a powder is spread. You place the rubber pad, press it using a specific pressure, and leave it there for a while. Afterwards you remove the pressure, shoots a photo of the rubber side with the square marks the powder made, transfer that photo to a computer, and have it calculate the ratio powdered area vs. non-powered area by literally counting how many pixels in the photo got this or that color and dividing one number by the other.
@mochdrew33643 жыл бұрын
That's what I would do in exam..
@svenminoptra7565 жыл бұрын
I used the 4 option.... I watched the video
@pratyushabala91365 жыл бұрын
Me too 😅
@winu19814 жыл бұрын
Sven Minoptra , 😂😂😂😂 I did the same
@nilsastrup89073 жыл бұрын
I Just loooooove the feeling when you can use so many different solutions to find the same answers. Keep up the good work!
@muhammadwaleedarshad44442 жыл бұрын
I once solved this really hard Q in class which no one could solve and then the teacher told us how to do it and his method was completely different than mine but we had the same answers.
@junaidseedat78523 жыл бұрын
The amount of work that goes into your videos is truly phenomenal 🙌
@naif2775 жыл бұрын
It's funny how calculus is 10 time easier than geometriy
@avhuf5 жыл бұрын
that's because the calculus way is the robot way, the geometric way is the intelligent way.
@SticklyDaKing5 жыл бұрын
avhuf why is it robot
@goyonman96555 жыл бұрын
No it's not
@shilpimitra53425 жыл бұрын
@@SticklyDaKing because u don't need to use a lot of ur brain , even a 10 th grade student can solve it that way given hr know all the formulas
@charli2165 жыл бұрын
Calculus is mostly used to program computers and calculators which uses the same definite way to solve one type of questions. Intelligent ways are much more diverse and allows shortcuts that cannot be discovered by machines. It also varies from one person to another, signifies creativity. Unlike calculus, geometry defines intelligences that a machine will never have. (Unless somebody invented artificial intelligence that will eventually cause global extinction.)
@tomcsvan5 жыл бұрын
I literally looked at the thumbnail and tried to solve it for 10 mins. My friend said “are you looking for something on the screen?”
@theunique1404 жыл бұрын
1! +2!+ 3! +...........25! divided by 13 then what will be the remainder left?
@joseluiscuervolopez-mora18144 жыл бұрын
I graphically solved it without paper after looking for hour and a half HAHAHAHA ocd
@GurmeetSingh08023 жыл бұрын
Area of intersection of two semi circles can be calculated by drawing all four semi circles inside a square. Suppose area of semi circle is A, area of intersection of two semi circles is B and area of the square is C than 4*A - 4*B = C. Because when you add areas of four semi circles together, each intersection will be counted twice so you have to subtract four times of the area of intersection in order to make it equal to the area of squire. For a square of side 10, the value of B is comes out to be 14.26. It is first half of the solution.
@DaBestNub3 жыл бұрын
I’m just gonna pretend I understand what he said
@baslelassefa66683 жыл бұрын
hahahahahaha so so good to know its not just me
@G-raverobber3 жыл бұрын
i could solve the yellow one with an easier formula but i will have to pretend to know about the blue one
@-Chicken_3 жыл бұрын
What his teacher hears: So if 3 - 2 = 1 it means that 1 is the answer What I hear: So if the power of xy squared divided by 5.73x10 to the power of -82 you can calculate the coefficients of angles bdgx2 and x over y to the power of 68 in an a standard form and that’s how you calculate the efficiency of booster 2 in a 2500 litre rocket...
@cubeeater64584 жыл бұрын
Your first "little lens" can be calculated much simpler, namely as the 5x5 square without the two other shapes, so that's 25 - (25 - quarter circle) - (25 - quarter circle), so that is a half circle of radius 5, minus 25 all in all, making it 12.5pi - 25. That's a whole lot faster than your "lens" calculation.
@--Za3 жыл бұрын
I've had a similar reasoning to do that part (square - 2 whole circles and then divide by 4). I wish there is a close way (substract areas) to solve the second part... i'm pretty sure there is one but i can't find it
@AlexKuz3 жыл бұрын
Isn't this basically a way he went in the second option?
@Nicolas-zf3pv3 жыл бұрын
His first “little lens” could be calculated in the way you showed, but what about the second “little lens”? You probably will need a different method to solve it, on the other hand, his method of the first “little lens” was applicable to the second lens, thus, saving him time and making the overall solution easier, at least in my opinion. How would you calculate the second “little lens”?
@m4rkus6183 жыл бұрын
I did the same.
@ruce92693 жыл бұрын
@@--Za did the exact same thing and the second part is bothering, you need to get the area of about 6.47 by using the circles but I cant seem to figure out how
@pratiksarve5 жыл бұрын
I put this in AutoCAD 😎😎😎 Ans - 9.7736
@ahmedmonjid56965 жыл бұрын
you are THE MAN
@mayanktomar50225 жыл бұрын
9.773570675
@pratiksarve5 жыл бұрын
@@ahmedmonjid5696 Thanks man
@pratiksarve5 жыл бұрын
@@mayanktomar5022 exactly
@-shadowz-59335 жыл бұрын
How did you measure the area of the shape? (I created the same things as shown in the video but I can't measure it)
@Retinetin4 жыл бұрын
I literally just finished calc 3 this morning so it was still very fresh in my head. I was thinking "oh, you could do polar coordinates and use single or double integrals (whatever you fancy), broken up by the intersection point, with the origin being in the top-right corner" I actually hate that these solutions were significantly easier and used a much more basic version of math
@bloodraven2.0364 жыл бұрын
Yea exactly, I was counting it by transforming into polar coordinates and in my head it was much easier with a double integral, than three basic integrals in cartesian
@randomthoughts60673 жыл бұрын
I'm proud to report I sat through the entire video without skipping. That alone is an accomplishment given how little I understand anything that was said.
@tomcruz98664 жыл бұрын
I just recently discovered your channel. I did the problem with both methods, the area subtraction using geometry (since that stood out to me) and the calculus way (because that just made sense integrals for the win). I set up the problems in my head and didn't particularly solve for an exact solution. Once that was done I finished watching the video. I m glad my physics/math brain is always on the ball great problem. Math is just awesome!
@JaydentheMathGuy5 жыл бұрын
Thanks, dude you made me realized I need to retake Calculus and Integration.
@mathpedia13 жыл бұрын
Solve this problem guys. This is a challenge for you. Problem given in my channel.
@GustaCakes3 жыл бұрын
Something tells me we may be able to solve this with a system of equations. I named each section with constants a --> f (with b being the objective), and got to b + e = pi*(10)^2/8. Only worked on it for a couple of minutes but I'm sure I can represent e (which would the the lower right section of the quarter circle) in terms of the total area of the square then I'm good! Thanks for sharing this Presh!
@MeTiMiTe2 жыл бұрын
Did you manage to do it that way, I'm really curious because I have been trying that myself but no results yet
@joseraimundo33872 жыл бұрын
I did the same and got to a matrix 6x6. I’ve tried solve it using Cramer’s rule but didn’t work. So I had to appel to the integral method and found 11,0743. I still didn’t watch the video.
@blooper5li4 жыл бұрын
I ended up a lot closer than I expected. I've been challenging myself recently to not use a calculator while solving problems, so when I tried using the geometric solution mentioned here, I ran into a major snag when having to calculate the inverse tangent. I ended up taking a best guess on it based on what looked right for the problem and ended up with a final answer of "9.9 or a little less". I'm surprised that I ended up using the correct method though. Usually geometry is my Achilles Heel for mathematics. I didn't even consider using calculus to solve for the answer, which surprises me given how much I tend to default to it.
@monkklein82825 жыл бұрын
One of the best math channels of KZfaq, greetings from Brazil!
@shyamsn21245 жыл бұрын
yes really
@l.3ok5 жыл бұрын
Papa Flamme ficou triste agora
@gustavol25005 жыл бұрын
Super exatas>>>
@gustavol25005 жыл бұрын
Xande god
@goyonman96555 жыл бұрын
Yeah This and 3Blue1Brown
@clieding5 жыл бұрын
I am still struggling with this problem so I haven‘t watched the solution- it is driving me nuts! I am not yet ready to give up. Wish me luck. 🤔🙄😳😠😩
@sushiboy6794 жыл бұрын
u done yet?
@drew73114 жыл бұрын
Affinizationz lmaoo 1 year later
@alistaw18664 жыл бұрын
I bet he stills solving it
@efhi4 жыл бұрын
Updates ?
@Mike-iz9kh4 жыл бұрын
I don't know of a way to do it without calculus. This isn't one of those "clever" problems that has a trick solution once you see it. Instead, it's a lot of grinding calculation.
@zangetsuzanpakuto52213 жыл бұрын
LETS GOOOO I ACTUALLY GOT ONE OF YOUR VIDEOS RIIGHTT ✊🏼😤 Damn I've never been so proud of myself lmao
@m4rkus6183 жыл бұрын
I used the 2nd method with some modifications. When calculating the blue shape I first calculated both of the sectors, and then I took the total "kite" area (= 50) and substracted one of the sectors from it to get the part of the other sector that is outside the blue lens. And then I simply subtracted this area from that other sector to calculate the blue shape. Seems to be easier.
@kayy28235 жыл бұрын
And i was there thinking i can do it in my head with my calc 🤣
@mathpedia13 жыл бұрын
Solve this problem guys. This is a challenge for you. Problem given in my channel.
@SuperMariocapo5 жыл бұрын
I solved this problem using calculus, it was the fastest and easiest way, in my opinion. I really liked the other two geometric forms of solving it!
@WoodyC-fv9hz Жыл бұрын
Hi Presh, many thanks for this gem. It's a lot more simple though. Focus on area PDA (via inner arc). I call it the battle axe. It's area is obviously 25. You instantly also know the area of PD, the double-sided symmetrical konvex lens which I call the fish. (done via computing semi-circle minus 25). Now work out area BCD (via point Q), I call it the "kite", like a hangglider (done by the "square" minus "quartercircle"). Thereafter you work out area QBC using year 10 high school maths (drawing a line from Q orthogonal to line BC) followed by integrating separately on both sides of this line "under" (here to the right of) the two arcs of the respective circles. Take QBC away from the "kite" and you get QCD, known as the cleaver. Take away cleaver and fish from already known semi-circle and yield PQD being 9.7735... Woody
@rohangeorge712 Жыл бұрын
wha...
@ShittingStar077 ай бұрын
Exactly how I did but got stuck at the QBC part..
@WoodyC-fv9hz5 ай бұрын
@@ShittingStar07 . QBC looks like a tail fin of a fish or a double-sided ramp. I come across this shape quite often . Even though calculus feels like cheating, the simplicity to work out the area is too quick and easy. I draw a line from Q orthogonal to BC and integrate both sides and add them together. It's merely 2 simple circles, easy. Two things to watch out for. We integrate above the circle not under it. Second thing, since there are two different radii, 3 component's change when writing down the integral, not two.
@cosmosapien5973 ай бұрын
@@WoodyC-fv9hz can it not be done without using calculus or trigonometry?
@yungstallion22013 жыл бұрын
1. 3D print the shape but give every edge the same height wall 2. Measure how much water it hold and how much red area holds 3. Red water divide by all water X100 4. Area of Square X Step 3 = Area of red
@justpaulo5 жыл бұрын
Wow! You really had a lot of work with this one! Great job! I used a mix of methods. For the 5x5 lens, I used geometry b/c its very easy to calculate: Area of 1/2 circle with radius 5 - 1/4 Square area. For the 5x10 lens I used calculus, but I turned the original pic upside down. So then it became integral of smaller circle from x=0 to 8 minus the integral of the larger circle from x=0 to 8. To solve the "sqrt's" integrals I had to look it up in a table of common indefinite integrals. PS: I also did it in the geometrical way, but my final solution uses arcCos function b/c I used the cosine law to determine the angle of the circumference arcs.
@johnnull13755 жыл бұрын
I did not calculate it, I guesstimated 10%, being a building contractor has it's perks ! ;)
@adi-sngh4 жыл бұрын
Lol
@cubeeater64584 жыл бұрын
"its" used as a genitive gets no apostrophe.
@SpaghettiRuin4 жыл бұрын
@@cubeeater6458 dude, get a life.
@hisham_hm4 жыл бұрын
whoa, that's great!
@robbrown75923 жыл бұрын
@@cubeeater6458 Ha ha. I couldn't do the maths problem, but like you I can see all the grammatical errors in the comments :-)
@ichigo4494 жыл бұрын
I solved this when I was a fetus in India.
@ihavetowait90daystochangem673 жыл бұрын
Thanks for making me feel like I learned both something and nothing in this video
@striker84454 жыл бұрын
I liked it at the end when he said "did you figured out this problem ?" XD Please have mercy
@thousandwater5 жыл бұрын
As soon as I saw this picture, the word "calculus " came to my mind, even though I had no idea how exactly...
@mathpedia13 жыл бұрын
Solve this problem guys. This is a challenge for you. Problem given in my channel.
@chrisj54433 жыл бұрын
I used method 1, except: first, I was too lazy to do the math for the larger lens, so used an online calculator for that (area=24.043), and second, I found the area of the smaller lens by a simpler method. Not having the graphics available, I describe it thus: the smaller lens is found by calculating 1/2(area of left-side semicircle) - 1/2( 1/2 the box area - area of upper semicircle), or 1/2(39.270) - 1/2(50-39.270) = 14.270. So large lens less small lens is 24.043 - 14.270 = 9.773.
@I_am_9root2 жыл бұрын
I've graduated high school 2 years ago and I almost forgot those math elements.. Now I remember that I was genius in math when I was a student and now I realized that my brain is rotten since graduation... Better study again. I've been wasting my time since graduation playing games and internet surfing... Thank you so much.
@kdmq5 жыл бұрын
I literally wrote a python code to do this computationally: start with an nxn grid. Imagine a circle at point (0,0) of radius n. (circle 1) Imagine a circle at point (0,n/2) of radius n/2. (circle 2) Imagine a circle at point (n/2,0) of radius n/2. (circle 3) Loop through literally every point in the nxn grid. Add to variable A if the point is: inside circle 1 AND outside circle 2 AND inside circle 3. The ratio A/n^2 is the percentage of the square containing the area we want. Multiply by 100 square units and you have the answer to the question. I blew n up to 5000 and waited about 45 seconds for my code to run and I got 9.77, so there is a "Red Green" solution lol.
@apocalypticbean5 жыл бұрын
share it please
@ansonchiu12065 жыл бұрын
What you did is known as monte carlo integration
@genroynoisis69805 жыл бұрын
GG
@husseinsaddamhussein28225 жыл бұрын
nice
@AdamAmbrus4 жыл бұрын
that seems unnecessarily brute force...
@jimsavino47295 жыл бұрын
This is solvable using geometry and algebra only. Algebra can find the coordinates of the right-most circular intersection using the general equation for circles and the known centers. Knowing that, a sufficient system of triangles can be constructed such that the desired area is obtained purely by addition / subtraction of triangular areas and arc segment areas. I will confess it took 2 hrs to come to this conclusion.
@ligaseptian66125 жыл бұрын
Exactly, i did it. And i got 9,78%
@kasra50965 жыл бұрын
It took me 3 hours using the same method!
@mahdi7d1rostami2 жыл бұрын
Same with me. As soon as I saw the picture I thought this is to complicated to think about. Let's just integrate and get it over with. But I knew for sure there must be a geometric solution.
@the-boy-who-lived11 ай бұрын
I got the area of the yellow area a differrent way: Area of the semicircle = 12.5π (Solve with πr^2 × 1/2) Multiple it with four 12.5π × 4 = 50π It is like you draw four semicircles inside the square. Or imagine as mirroring the two given semicircles. Now you can see it covers the whole square and also the yellow area 4 times overlaying. Which means 50π = area of the circle + 4 × yellow areas 50π = 100 + 4y (y=yellow area) y = (50π - 100)/4 y = 25/2(π-2) y = 12.5π - 25
@guycaats3 жыл бұрын
2:02 Solution using geometry and trigonometry 6:49 Longer solution using geometry and trigonometry 12:06 Solution using calculus (integrals)
@takyc78833 жыл бұрын
I did integrals but I’m finding a common theme. Whenever looking for an area of a circular shape, find a right angle triangle that splits the needed area into a right triangle and a proportion of the circle
@bhavyaramakrishnan8014 жыл бұрын
1. Suppose it was given the rectangle has length 10. First we have to prove the rectangle is a square. 2. Also the yellow lens area is not necessarily symmetric is it if it is a rectangle? 3. This applies only for the square case.
@mathpedia13 жыл бұрын
Solve this problem guys. This is a challenge for you. Problem given in the link below. kzfaq.info/get/bejne/ps2Hq5p0ztaqnKM.html
@Gustavo-gd9bz3 жыл бұрын
You can divide the square in to 4 smaller squares each with a area of 25 and assume the circles radius to be 5 and 10 by completing them, the result is similar and can be calculated by normal math.
@rmsgrey5 жыл бұрын
As an observation, the formula found for the area of a lens in the video is for the special case of a lens where the two circles meet at right angles - in general, you won't have right-angled triangles, and end up with a longer general formula (the standard version is given in terms of r and R, the two radii, and d, the distance between the two centers)
@goyonman96555 жыл бұрын
Can you state the longer one?
@we-are-electric14455 жыл бұрын
Absolutely. It's only going to be a right angle if you have a tangent which, as you say, is only in one special case. I'd stick with the calculus !
@goyonman96555 жыл бұрын
@@we-are-electric1445 But being bent at an angle other than 90 degrees would complicate the Cartesian plane needed for the integration
@we-are-electric14455 жыл бұрын
@@goyonman9655 It is in two dimensions so the integration should be straightforward. I haven't checked the proof. The narrator seemed to be skipping bits from the part I listened to and his calculus explanation didn't seem clear. The key point is equating two of the curves to determine the x,y limit points through which you need to integrate. When people skip bits of an explanation most usually it's because they are so clever they expect everyone else sees the missing bits as obvious or they don't fully understand the proof. If he comes back and corrects me then fine but at least i hope he comes back with more information.
@goyonman96555 жыл бұрын
@@we-are-electric1445 Remember the dimensions of the square gave him values of points on the axes and how to pinpoint their values on the plane
@andrejsasd89043 жыл бұрын
When you showed that the length of the side of square is 10, my first guess was "the area is somewhere around 10". And then you showed that it is around 9.77. :D
@aswinos64002 жыл бұрын
My hearty thanks:from India
@Rottwiler443 жыл бұрын
i just drew this up in Fusion360 and had it measure the area for me.
@LON0093 жыл бұрын
"So let's simplify" Me: Yes, please *complex equation turns into another complex equation* Me: ok
@WhySoSquid5 жыл бұрын
My ignorant younger self took AP Stats instead of AP Cal..so I did this the long geometric way, and essentially just nodded my head as you narrated the on-screen calc operations, like, "Yes, the audio appears to be in sync with the video here," so, long story short... 🙏 I appreciate your videos, which make me wish I'd taken more maths courses at university, because I always enjoyed the subject and I ought to have continued to be good at it (Well, that wasn't very short, was it?) ✌️
@candidfever34453 жыл бұрын
I used hyperoperated calculus with stable equality with a trig failsafe, also including operation successorship. This method is unbeatable.
@jackychanfang74482 жыл бұрын
Ngl its an emotion After 2.5 hrs of constant doing math i did itttt Yess i did it
@miikey_lol5 жыл бұрын
Wait a second, this video was a month ago. Was it only for patreons or something?
@MindYourDecisions5 жыл бұрын
You posted before my comment appeared...The first comment is from 1 month ago because I posted it to Math StackExchange where I received great help: math.stackexchange.com/questions/3016718/a-way-to-find-this-area-without-calculus Early comments also come from Patreon, as I do my best to give early access to supporters on Patreon: www.patreon.com/mindyourdecisions And finally, thanks for 1 million subscribers! We are building one of the best mathematical communities in the world. Thank you.
@mathpedia13 жыл бұрын
Solve this problem guys. This is a challenge for you. Problem given in my channel.
@corpo86303 жыл бұрын
why this have 69 likes ?
@kagez65155 жыл бұрын
“Uploaded January 10, 2019” 1 month comments W A I T
@MindYourDecisions5 жыл бұрын
You posted before my comment appeared...The first comment is from 1 month ago because I posted it to Math StackExchange where I received great help: math.stackexchange.com/questions/3016718/a-way-to-find-this-area-without-calculus Early comments also come from Patreon, as I do my best to give early access to supporters on Patreon: www.patreon.com/mindyourdecisions And finally, thanks for 1 million subscribers! We are building one of the best mathematical communities in the world. Thank you.
@vincentstormz18845 жыл бұрын
And that my boii is how a tough problem looks like
@Aman-br1ph4 жыл бұрын
@@MindYourDecisions Could you pls gimme some information about Math stack exchange
@beginneratstuff Жыл бұрын
I remember a few years ago I wasn't able to solve this. I was able to solve it today having learned calculus. The geometric way requires less calculations, but the critical thinking involved in that method would have taken me longer to be honest. So the calculus way was the fastest way to solve it for me.
@luisaguilar5343 Жыл бұрын
I've never felt more smooth brained in my life.
@maalikserebryakov Жыл бұрын
Just be a calculus loser like me lol
@rio_agustian_5 жыл бұрын
*3 Ways to Get Depressions (Insanely Work)*
@strangebird59744 жыл бұрын
After watching the solutions, I realize that I'm simply mathematically undereducated, I didn't have the tools to solve it with what little trigonometry I remember from school. I guess, I'll have to start from scratch with basic maths if I want to be able to tackle problems like these... Oh well, it was fun trying to derive what I could with what little I could remember.
@markjust863 жыл бұрын
🤯 I get the second solution best out of all of them but I wouldn't have got there in a million years and I wouldn't be able to do it even now without watching this again!
@georgemarklow46833 жыл бұрын
The way I did it was drawing the diagram and putting A, B, C, D, E and F into each of six parts of the jigsaw puzzle, with B being the shaded bit. If we take half of one side of the square as r, the area of the square is 4r2 then express B = 4r2 - A - C - D - E - F and you can find other relations where two of the letters add together to make half an area of a circle etc etc and eventually all other variables cancel out to give the answer.
@kevinmartin77605 жыл бұрын
The second method seemed to me to just be the first method worked out twice with specific values for a and b. In both cases you find all the triangles etc.
@mathpedia13 жыл бұрын
Solve this problem guys. This is a challenge for you. Problem given in the link below. kzfaq.info/get/bejne/ps2Hq5p0ztaqnKM.html
@sushirl30365 жыл бұрын
Could you work out the area of the semi circles and the quarter circle, then add them up, then take away the area of the square, then since you have two layers of the required area then dive it by 2?
@chaitanyaatale.56263 жыл бұрын
0:53 yeah
@mariagabrielasouza3564 жыл бұрын
Hello! I am from Brazil and I love your channel. Thanks for everything
@TrevorAllenMD3 жыл бұрын
MCAT skill: “idk looks like around 10% or so” Mathematician / physics skills * 25 minutes of work later = 9.77 *
@chetansaini78582 жыл бұрын
i got 856/75
@Sam_on_YouTube5 жыл бұрын
I looked at that and thought: It is pretty straightforward with calculus, though it would take a while with multiple integrals. With geometry, that's tough. EDIT: I wrote that before watching. That makes me feel better.
@orchoose5 жыл бұрын
3 definite integrals if i count correctly that is if you chose 0 for y at conviniant position, not even watching :D
@rohrxd5 жыл бұрын
Sam two double integrals, the region can be broken down into two type 1 or two type 2 regions.
@theunique1404 жыл бұрын
1! +2!+ 3! +...........25! divided by 13 then what will be the remainder left?
@Sam_on_YouTube4 жыл бұрын
@@theunique140 0. 13 is a factor.
@Sam_on_YouTube4 жыл бұрын
@@theunique140 Slightly more interesting variant I just thought of: Divide by 13^13. Same answer.
@vsdktbkm50123 жыл бұрын
For the calculus solution, I used polar coordinates. Rotated the figure and shifted the origin to the point where the left, top point (0,5) is now located at. Doing so, all the curves pass through the origin and r-theta functions are easy to set up. Used A= 0.5 x integral of r^2 d theta. All the cartesian equations of circles can be converted easily to polar x = r* cos(theta) etc. This is a shorter and less painful method than using cartesian system shown here. All the angular limits are easy to find using regular trig/geometric formulae.
@GillesF313 жыл бұрын
The method by the integrales is great !!! And it's a good mean to understand how powerful are the integral concept and tool !!! Very nice video !!!
@drachenreiter12963 жыл бұрын
I used an calculator. Definitely the best method.
@MuriloPerrone2 жыл бұрын
Here is another way of showing the geometrical method: For the semi-circles, we have the circle area formula of πr², so: half circles area = 25π/2 = 12.5π quarter circle area = 100π/4 = 25π Considering that the small lens goes between two identical circles, we can claulcat it as: smalllens = semi_circle1 + semi_circle2 - kite smalllens = 12.5π + 12.5π - 25 smalllens = 12.5 x (π-2) or smalllens = (π-2) x side² / 8 And for the biglens we need the lens formula: biglens = side² x (6 x arctan(0,5) - 4 + pi) / 8 f = side² - 12.5π - 25π + biglens Then we can solve: Answer = biglens - smalllens
@jiahgl2 жыл бұрын
okay, at the end of the video, you asked if i got this question and what method I used, but I did Not in fact get an answer, but I had the thought process of what methods I would have used which were all correct. I haven't been in math for two going onto three years, but I knew and followed everything you were explaining. Made me smile
@CurtFitz3 жыл бұрын
For solving for that yellow portion you can take the area of a square 10x10 then subtract the area of a circle r = 5 divide the num by 2 it will equal 10.75 then take the half-circle givin and subtract the 10.75 this will give the area of 2 of those yellow shapes so divide by 2. I think this may be easier to follow example that more people would be able to understand. I realize that what I said above may be hard to follow but with pictures, everyone would be able to follow. However, I have been unable to solve for the area of the blue shape using only basic shape areas and/or without advanced geometry knowledge. Originally, when I tried solving the problem I was trying to take the half circle and subtract the yellow shape and DQC. Would be super interested if anyone were to solve this using only the basics of geometry.
@francescosaccomanni90243 жыл бұрын
I also suspect there may be a solution that doesn’t involve trigonometry, but I’m still looking! I used the same method as yours to get the first lens
@bibhuprasadmahananda69865 жыл бұрын
I approached it with calculus. BUT the geometric solutions were elegant.
@markcross1095 жыл бұрын
Did you get the right answer or you just tried to solve it?
@mathpedia13 жыл бұрын
Solve this problem guys. This is a challenge for you. Problem given in my channel.
@andrewwwmnt5 жыл бұрын
Love your vids! Please don't stop!
@victorpetrescu13 Жыл бұрын
I think there is a simpler method that uses no trigonometry, pls. correct me if I miss anything: 1. Compute the yellow area as in method 2 2. We can compute DPA area as the semicircle minus the lens we already calculated 3. We can compute DPC area in the same way (also they are equal - symmetry) 4. We can compute APCB area as the square minus lens minus DPA minus DPC 5. We can compute DBC as square minus DAB 6. We can compute DPABC as square minus left semicircle 7. Now we can form 4 equations with 4 unknowns: - DPQ + DQC = DPC (known from point 3) - DQC + CQB = DBC (known from point 5) - APQB + CQB = APCB (known from point 4) - DPQ + DQC + APCB + CQB = DPABC (known from point 6)
@KucingAhong3 жыл бұрын
- Draw it on CAD software - select the boundary - Find the area
@DerKleineThilo3 жыл бұрын
Took me a full hour, now i finally can go to bed
@sonofsarek5 жыл бұрын
It’s been 20 years and I still remember soh cah toa.
@philbytan2845 жыл бұрын
Mah man!!
@mathpedia13 жыл бұрын
Solve this problem guys. This is a challenge for you. Problem given in the link below. kzfaq.info/get/bejne/ps2Hq5p0ztaqnKM.html
@epimaths3 жыл бұрын
Thank you for your helpful lecture. The method of subtracting area to calculate the area of the figure to find.
@mohabatkhanmalak11614 жыл бұрын
I did't solve it but just watched the solutions. Very interesting, and of the three I think the second solution is simpler and better. The Calculus solution is very drawn out and would need a person who is good at it - we all can be good at Calculus, just keep practicing and memorize first pricipals. Thanks for posting and really enjoy your maths videos.
@gotchabitch73615 жыл бұрын
*10* *9* *8* *7* *6* *5* *4* *3* *2* *1* *0* *and that ends the official countdown of my brain cells*
@mathpedia13 жыл бұрын
Solve this problem guys. This is a challenge for you. Problem given in my channel.
@bayusetiawan1814 жыл бұрын
He said "simplify" Me : "How?"
@typingcat3 жыл бұрын
kzfaq.info/get/bejne/htKjipWZyZaagmQ.html
@hurtee18074 жыл бұрын
I know I am late to the party, but I have one small suggestion. You could make your life a little bit easier during the trigonometric solutions when you assume the square to have a length of 1 and at the end multiply the solution for B by 100. This way you get rid of a few r^2 since r=1.
@zakthefurryfeline88652 жыл бұрын
I gave my math teacher this problem at the end of last lesson and she, her sixth form class and the head of math spent their whole lunch and the entire sixth form period attempting it, she had to watch this video to figure it out
@Trugoy10005 жыл бұрын
My head hurts now.....
@COZYTW5 жыл бұрын
I feel like if I just studied, revisited and rediscovered the maths I learned in polytechnic I'd be able to solve using both trigo & calculus. I really need a jumpstart course on that.
@mathpedia13 жыл бұрын
Solve this problem guys. This is a challenge for you. Problem given in my channel.
@tfpslegend77172 жыл бұрын
The geometric stuff is so confusing, calculus is so much easier.
@borjaroca12624 жыл бұрын
Intersection between two equal circles in that position will always be (pi/2 - 1)*rˆ2. You can easily deduce it drawing the combination of the two circles into a square of its diameter.