Derivative of Area is Perimeter?

[@mepkn]

I always thought the case with circle was just mere coincidence, so glad that I was proven wrong.

[@MrRogordo]

Missed your videos, hope your math degree is going great

[@PranavViswanathan]

Reminds me of an Aleph 0 vid about Stokes’ Theorem on Manifolds and how he talked about how taking the relationship between derivatives and boundaries.

[@sam08090]

The converse is also interesting. Circle with perimeter 2*pi*R integrated from 0 to R sweeps an Area of pi*R^2. Sphere with surface Area of (4)*pi*R^2 integrated from 0 to R generate a volume of (4/3)*pi*R^3.

[@roygalaasen]

I have always been pondering on this. I even tried to ask a former friend of mine whom I used to look up to that was a math wizard, but he just laughed and cut me off with no more explanation, so I just dropped the thought, though it never really left me.

[@luketyler5728]

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From Barranco Lima Peru good job

[@maheshpatel7691]

Wow! I wondered about circle, but didnt delve this deep

[@ezras7997]

That’s a beautiful presentation.

[@jamesbentonticer4706]

Sure is.

[@oxbmaths]

Nice video! Sequel: Derivative of Volume is Area :)

[@tomkerruish2982]

Nicely done! Personally, I would've argued using infinitesimals, but that's rather hand wavy. YMMV as you young'uns say. Here's to still hoping you can attend in person next year!

[@sheaisabutter]

thats a sacrilegious way of holding a whiteboard marker, sir

[@kyuubinokitsune13]

Awesome video! Do you have any references for the general case of any Jordan curve??

[@BleachWizz]

Respective length. Good concept, good concept indeed.

[@titassamanta6885]

Coincidentally, one hour before this video was recommended to me, I discovered the sam.

[@sal100nx7]

Muy buen video :^)

[@omargaber3122]

Wonderfull ,,,thank you

[@joaofrancisco8864]

Very nice!

[@HolyG-sus]

Can u calculate the formula for volume of sphere using any formula of circle Damn u r genius...

[@jamesbentonticer4706]

Yeah I think he really is. Like no joke.

[@lemon.linguist]

can this be generalized to higher dimensions or no?

[@MuPrimeMath]

The "volume" of an n-dimensional shape scales with r^n, so working through the math as in the video we find that the length must be r = nV/A, where A is the "surface area". The video is the special case n=2. For example, in 3 dimensions we obtain r = 3V/A. One can compute directly that this equation is satisfied for a sphere, which is why the derivative of a sphere's volume is its surface area when we use the radius as the length measure.

[@ilikeandlovemathsandothers8880]

Namaskar from shyamal Bhaumik M sc in Economics

[@Nickle314]

Next lesson, tensors ...

[@robertflynn6686]

In calculus the def of derivative is inverse the integral def. and visa versa.. the undo each other. Integrals are areas under or interior to functions. Derivatives that reduces back to the functions

[@angelmendez-rivera351]

Well, that is not accurate. The proper relationship between derivatives and integrals is given by the generalized Stokes' theorem. It should also be noted that the derivative operator is not an invertible operator.