What’s the area? 

Why?

Gyattt

​@@bebektoxic2136 search the female reproduction sistem

U guys are sick bro

Get medication

did you actually? You'd have the curve from the upper circle where the integral starts/ends at the two intersections of the upper circle. And the integral interval is split into two since there are two segments with different functions given the two lower circles. However, since they are the same, we only need to compute one half.

based

what did you integrate over

@@rasuru_dev likely x, left to right area determination

​@@rasuru_dev for simplifying I considered the area of the section between the straight line that contains the centre of the triangle and the left tangent point (the point tangent to the upper circle and the left one). Describing those functions with the centre of the left circle un (0,0) would result in the [1/2 , 1] as the set of integration. Then you multiply that area by 3 and you obtain the same result!

I hope you realize how many people feel exactly the same way xd

hey, so totally out of context here but.. my usual depressive episodes are during 3 pm 😅 coincidence!!

@@LordNaver Everyone has their own individual rythm, so beautiful ☺️

@@LordNaver for me it's because I can distract myself with work or something during daytime but I dread the nights because I'm alone with my thoughts

@@user-wp4vs1ug6z interesting.. quite the opposite for me.. At night I feel quite calm, and composed, there is a sense of confidence in my thoughts. whereas in the afternoon, it's hot and dry, the most mundane and boring part of the day.. it is somehow low key depressing.. interesting.. to see different perspectives..

Only the rear part

PFF FR

😂😂

@@linuxp00 that's the front part. The rear part is just a line.

And thank you!

It's not a man's g-string, it has no extra circle in the bottom part

😂😂😂

Not Nicola Tesla 💀

isn't calculus amazing!? 😍

They use this question to mock mathematics virgins in exams.

🤨

Yep. M-hm. Definitely. Well. I see it.

"Everything reminds me of her"😢

No more internet for you.

Aw man i thought you meant the pizza wedges lol

💀💀

Bro 💀 "ram bhakt"

that's what I gonna sa-

area of sector how?

it's the only way...

Actually I don't think so, you can divide the shape into two pieces vertically then using integral and the equations of the remaining tangent circle and half one on top, remembering we have the radius of each and the two tangent points. So what about that? Edit: not sure.

Same goggypoggy.

@@savitatawade2403You can also connect the tangent points of the circles to form a triangle and then subtract the area of three segments from its area (as opposed to subtracting the area of three sectors from a triangle formed on center points)

SAME BRO

What?

😏

😅

Only legends will understand 😏😂

Lol, thats what I was thinking. The brackets make up a part of that area too.

😂😏

It's not different mind it's dirty mind

Bro reminded of an underwear😂, isn't it?

Yes, apparently your mind is not that different

@@joshsingh1111 many people did - and some pointed out it gets better when you include the ( )

The area will satisfy more💀

​@@mr.unknown1070💀👍

Wht made you think of hexagons at all though or remember an apothem even? Thanks for sharing.

@@leif1075 that's the only plane filling shape that fits between balls stacked that way. Also, they're the bestagons. And I also know the formula for the area of both a circle and a hexagon, and I have a faint clue of subtraction. About the apothem, I really like Scrabble. And maths. And hexagons.

@@mennolente4807 That's pretty dope!

nice!

Cool

I was on the math team a lifetime ago in high school. Little things like this let me relive the good ol’ days lol.

It is because it's class 10 level question Of circles chapter and it is level 5 question😅

Yet you could not solve it. Don't be overconfident.

@@JitendraSingh-lr4nu It's okay if you couldn't do it but don't randomly judge people mate. It's a pretty simple question from grade 10

@@JitendraSingh-lr4nu What makes you think they couldn’t solve it? The answer was provided at the end of the video. Why would they feel the need to include it here?

Area of the thong

Sweet! I had the same idea. Then thought maybe it was a long approach. I'm glad I wasn't mistaken for it to be a solution 😊

Why would younthinknlf hexagons at all just wondering? And not squares or rectangles? I can see maybe forming a hexagon using all three circles..but why only in one..seems kind kf out kf nowhere?

@@leif1075 I didn’t think hexagons immediately, what I did was take the very center point of the structure, and draw 2 lines to any 2 of the 3 points of tangency between the circles. That forms a shape which is 1/3 of the center area, but also happens to be 1/6 of the area of a hexagon circumscribing the circle which has the 2 chosen points of tangency, minus the area of the circle.

wtf

@@rubykanima I have no idea what I was saying, sometimes I get drunk and get especially good at math Glad to know it was apparently relevant though I no longer understand how that works

​@@lillii9119I would definitely buy you a beer if I bump into you in real life

Make it polar and integrate from 0 to 2π/3. Triple that for the area.

unless u do some quirky math, that s not a simple integral

Exactly what I thought!

How do you know sectors will form 60°

@@tariqwaheed7429 He literally said "equilateral triangle". Anyway, it can be inferred cuz all 3 circles have same diameter.

that is exactly what i was thinking in my head

​@@tariqwaheed7429same distance bw center of two each circles

Show us please please

area of triangle - are of unit circle the sectors make a full circle and what you have written will give answer in -ve

Wrong, you need to switch those terms.

@@Ruktiet true, but you can also assume negative areas, like distances, as possitive and kill their minus sign

The area of bigger triangle connecting centes of circles -- Aera of 3 sectors (how will it give negative answer , you can clearly see the area is small than the triangle)

@@Ruktiet it's correct wdym

Funny. I got the same thing about 30 seconds later.

Yes 🎉

You all assumed that r is 1 except me ?😅

​@@JoJo-jj6iddw i didnt either r^(2)[3^(1/2)-(π/2)] looks less neat buts much more useful

Damn u got this

😂😂😂

stay strong not HARD

@@udayraj6976 stay hard and strong!

​@@dyltanwhy do we share the same brain cells 😂😂

Yes, this explains it quite clearly, while the formula doesn't, for those who aren't used to visualize formulas.

He said unit circle so R = 1

Yep, same. The general case would be, Area = R²( √3 - π/2) Where R represents the radius of circle assuming all of them have same radius ofcourse. Edit: if radii of all the circles are different, then doing it by calculus would be better as the method shown in the video would get *very* complex.

A line from the center is always going to be 90° to a line tangent to a circle at point of tangency. Since 2 circles share point of tangency, a line from one center to another is always a straight line.

how?

​@@arnabchatterjee1601 We did this in middle school so I remembered how to do it (it was for some math competition, pretty low level one, I think almost everyone got this question right, we had like 3h for 5 questions so we had a lot of time to think lol). Of course, the answer was different, but I remembered how I solved it (I actually think we had to find the ratio between the area of that little weird part in comparison with the area of the 3 circles (or just one, no idea really) with respect to r as the radius wasn't given and was just labelled r). As for why I was able to do it in my head: because I know 2 very simple middle school formulas: the formula for an equilateral triangle which is a^2*sqrt(3)/4 and since the side was 2*1=2 I just put that number there instead of a and got 4/4*sqrt(3) which is just the sqrt(3) for the area of the triangle. After that I just simply did the "part of the circle area formula, no idea what the english name is" which is pretty simple: r^2*pi*60/360 (because they were all 60 degrees cuz they're equilateral triangles) since r=1 (cuz unit circle) it's just 6/36*pi which is actually 1/6*pi which is the area of each circle part and after multiplying by 3 you get 3/6*pi which is just pi/2, that's the area of the part of the triangle that you do not need, after that just subtract sqrt(3)-pi/2 and that's the answer I got in about 30 seconds. Again, I did this all in my head, I actually pulled up my scientific calculator app on my phone, but ended up not needing it as it was just so simple. Also, I knew this procedure pretty well so it was nothing special, it was one of my favorite middle school "low level competition" problems, I never really did any high level competitions, I just dabbled in them easy ones, and this thing was damn near the easiest thing they'd ever put on them, though I would have needed a calculator had the numbers not been so nice and clean (which you do not get at our stupid competitions, one of the reasons I didn't like them very much). Sorry for the long reply btw lol.

If r = 1, your result is 2√3 - π/2.

It's actually: (r²(2√3 - π)) / 2

How did you get that 4? The area for an equilateral triangle is √3/4•s² (where _s_ is the length of any of its sides). For the general case for this scenario, s=2r, so we get √3/4•(2r)² = √3/4•4r² = r²√3. Subtract the 3•(π/6)•r² = (π/2)r² for the sectors, and we get r²√3 − (π/2)r² = (√3 − π/2)r² = (2√3 − π)r²/2. Somehow, you got double the actual area for the triangle circumscribed around the space, giving an extra factor of 2 for that particular term in the expression.

@@brianhull2407 I don't have my notes anymore but as I don't know the formula for the area of an equilateral triangle by heart, I worked it out myself, and either accidentally missed out the /2 in sin(60°) = √3/2, or I forgot to divide by 2 when doing b × h / 2. either way it was some trivial mistake when working out the area of the triangle, my bad

for the record, I didn't do the same method as in the video, I did a smaller triangle between the contact points of the triangles, and subtracting the areas of the chords

Glad I'm not the only one ha ha

Is 1 order of magnitude out considered close these days?

@@Grizzly01-vr4pn oh my mistake I meant 0,1612. I actually did the calculation one more time and got 0,1612544807038 which is only of by 0,0000000000702 👍🏼

Because the angle of the pink wedge is 60° which is 1/6 of 360°

The triangle is an equilateral triangle. This has equal angles of 60⁰. Thus, the pink areas are equal. This is r²•π•(60⁰/360⁰) = r²•π•(⅙) r = 1 Gives π/6

Equilateral triangle has Interior angle of 60° each. A circle has 360° , then the sector is 60°/360° = 1/6 of the circle.

Thanks

Greetings@@neitoxotien2258 , This part, i.e., "A circle has 360°" I am trying to interpret. How do You measure this 360° angle in this particular case?

Probably possible :)

yes for sure.

Nothing like that even i read external So don't be overconfident on a indian.