Circle area from peeling circumferences (pi day short)

In this short, we show one way to find the area using using the method of exhaustion by unrolling successive circumferences of nested circular shells. In this manner, the circle area gets transformed into the area of a triangle with base 2pi times r and height r.

#math #manim #visualproof #proofwithoutwords #circle #circlearea #archimedes #radius #area #areaofcircle #pi #piday #shorts #circle #archimedes

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[AGsolomank]

my dyslexic ass thought it said peeing in a circle

[DissonantSynth]

This has always been my favourite proof

[tamirerez]

It's true that you can't square the circle, but hey! You can triangle it...😉👍

[iquemedia]

bro stranglehold caught me so off guard lmao

[hifdhhdddgjresd]

That's the basic idea behind integral calculus

[_im_also_here_]

"CIRCLES. ARE LIKE. ONIONS."

[mebaaibokl.nonglait]

Love it.. been struggling to find out how they arrive with the formula for area of a circle

[dranandamay]

Simplicity is the beauty of Nature ... and of Maths ... we only need to see it ❤

[TheBestGuitaristForReal]

Visual representing is so important for understanding the concept.
In textbooks we don't really see how the formula 2πr(r+h) came to be.

[elpman]

A genuinely awesome video....Nuge and math... together

[anjalidwivedi]

You know what this means, a circle is merely a triangle with height = r and base = 2πr ( obviously for area)
And there I broke maths... A circle can have vertices, you just gotta change your perspective..😀😀

[sleha]

Damn that's new to me!
And I loved it

[davidnoll]

I think it needs a little more clarity that the lengths each just so happen to be linear when stacked. They could have made a an arc of some kind too and i wouldn’t have been too surprised

[ZantierTasa]

oh yeah... because circumference is proportional to radius, it does form a triangle with straight lines. Very neat!

[weirdo]

Also Getting area by integrating 2pier from 0 to r...

[avr]

Good music and math?!?? There is nothing better

[vennstudios]

I think I can make a words only simplification

Since the area of a circle is just a bunch of smaller concentric circles we could say as the radius decrease linearly
the circumference decreases linearly

hence we can make a triangle which has the base of the largest Circumference and the height of the radius

thus you get πr²

[gaopinghu]

Well, you'd have to prove that when you peel a layer, the next one is always shorter by the same amount. It isn't hard, but should be specified.

[zohar]

Nice, but how do you know you will get two straight lines? ( 2 sides of the triangle)

[treetop]

Interesting, but you'd have to account for "turning a curve into a straight line" because Hilbert