Derivative of Area is Perimeter?

Epic Math Time's video: • When is the derivative...
When is the derivative of area equal to the perimeter? In this video we solve this calculus/geometry problem for any shape. Then we look at regular polygons and get some very interesting results!
Calculus Problems playlist: • Calculus Problems
0:00 General case
6:21 Examples
9:26 Regular polygon case
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Music: C418 - Pr Department

[@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.

From Barranco Lima Peru good job

[@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.

[@sal100nx7]

Muy buen video :^)

[@joaofrancisco8864]

Very nice!

[@omargaber3122]

Wonderfull ,,,thank you

[@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]

.

[@maheshpatel7691]

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

[@oxbmaths]

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

[@sheaisabutter]

thats a sacrilegious way of holding a whiteboard marker, sir

[@titassamanta6885]

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

[@ezras7997]

That’s a beautiful presentation.

[@jamesbentonticer4706]

Sure is.

[@BleachWizz]

Respective length. Good concept, good concept indeed.

[@kyuubinokitsune13]

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

[@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!

[@ilikeandlovemathsandothers8880]

Namaskar from shyamal Bhaumik M sc in Economics

[@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.

[@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.