Circle Area (classic visual proof)

This is an animation of a classic visual proof showing how to find the area of a circle by using more and more wedges and arranging them in a rectangle.
#manim #mathshorts​ #mathvideo​ #math​ #geometry #mtbos​ #animation​ #theorem​​​ #visualproof​ #proof​ #iteachmath #mathematics #circle #area #infinite
This proof can be traced to both Satō Moshun and Leonardo da Vinci (see Smith, David Eugene; Mikami, Yoshio (1914), A history of Japanese mathematics, archive.org/details/historyof..., page 130-132 and Beckmann, Petr (1976), A History of Pi, St. Martin's Griffin, page 19).
You can also read more about this in a great NYT article by Steven Strogatz: archive.nytimes.com/opinionat...
To learn more about animating with manim, check out:
manim.community
Here is the source code for this animation: github.com/Tom-Edgar/MVPS/blo...
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Music in this video:
Epic Adventure Cinematic Music | MOVIE by Alex-Productions | onsound.eu/
Music promoted by www.free-stock-music.com
Creative Commons Attribution 3.0 Unported License
creativecommons.org/licenses/...

[@forthrightgambitia1032]

Archimedes made the first post 2250 years ago.

[@MathVisualProofs]

Yes. But not this way :)

[@hkayakh]

Seeing the circles that were split up a lot and unfold was satisfying

[@MathVisualProofs]

Yes, fun to be able to do so many at once :)

[@OnlyTheAzure]

Bro is doing Math to his Battle music

[@MathVisualProofs]

always... :)

[@ShellyNoelly]

Beautiful

[@MaheshKumar-dn2hb]

Thanks!

[@kutub-uddin4429]

Amazing

[@ccona2020]

👌 Perfect. Thanks

[@jett717]

Cool music, great video!

[@user-ru2jr6ti6n]

I love this :)

[@MathVisualProofs]

:) Thanks!

[@mtr-math]

Sir I watch every video of you. Every video we make is awesome. Requested to make a video on sphere how to calculate volume and area

[@SuperYoonHo]

Thank you!

[@MathVisualProofs]

Thanks for watching :)

[@SuperYoonHo]

@@MathVisualProofs 🙏🙏

[@gustavoruiz5637]

Excellent video! I really like the part where you animate both halfs of the circunference as the rectangle long sides = Pi * r I didn't saw this key concept present in other videos thus making it harder to understand where the formula comes from for kids that are trying to understand this for the first time. A few years back (and even today) all this concepts were taught only as a formula to remember without explanation about where it came from, now there is a visual way that really helps to undertand. I wish this can be run from Jupyter notebook, it shows some errors such as "name 'ParametricCurve' is not defined" Any help on this? Thanks!

[@MathVisualProofs]

This is created with manimgl. I think ParametricCurve has been changed to ParametricFunction. Also, Tex has been changed to MathTex.

[@Asifur_Rahman]

Thanks a lot for these type of awesome video...

[@MathVisualProofs]

Thanks for checking them out!

[@Asifur_Rahman]

@@MathVisualProofs We want more videos like this, please...

[@MathVisualProofs]

@@Asifur_RahmanI have lots of the channel. Check them out

[@Asifur_Rahman]

@@MathVisualProofs Okay Sir, Thanks for your reply

[@Byynx]

You should make videos where you explain how you do these things on shaders.

[@timfieldsend816]

The pacing of this is excellent. The music is still a bit overbearing. I appreciate that I may be missing a musical "joke" though. Excellent graphic as usual.

[@hive6157]

nice

[@MathVisualProofs]

Thanks!

[@KaliFissure]

that last touch with the line segments of halved circle unbending and forming rectangle.....👍 is there a name for a rectangle of those proportions? the "squared" circle?

[@MathVisualProofs]

Maybe better to call it "rectangled" circle? I don't know of any standard term though. Thanks!

[@User-54321n]

Wow ❤️

[@MathVisualProofs]

:)

[@forhadahmed9231]

Amazing. I like it.Can you share PPT of this video?

[@MathVisualProofs]

Don't have this in PTT form, sorry.

[@mindgame1468]

Could you share as manim code pls. I want to learn this deepest part of my heart.🙏🙏🙏

[@MathVisualProofs]

The link is in the description.

[@monoman4083]

super..

[@MathVisualProofs]

Thank you

[@user-tr7ys1ym7g]

It's an interesting video. Can you share your code? I want to learn it

[@MathVisualProofs]

Thanks! Here is the code : github.com/Tom-Edgar/MVPS/blob/main/circlearea-10_10_2022.py (not commented; sorry)

[@user-tr7ys1ym7g]

@@MathVisualProofs thank you so much

[@shezanahmmed5582]

Which software did you use for this simulation? Could you please tell me about it?

[@MathVisualProofs]

This is created with manim, which is the python library created by 3blue1brown.

[@shezanahmmed5582]

​@@MathVisualProofsThank you so much for this information.

[@maynardtrendle820]

Noice! 🐢

[@MathVisualProofs]

👍

[@wawawuu]

The music is unbearable in what is otherwise an excellent video.

[@MathVisualProofs]

I realize my choice of music is polarizing but I’m sticking by the drama. :) thanks!

[@kimba381]

One needs to be careful with these "visual" proofs, an identical approach to the area of a sphere leads to A = (πR)^2

[@MohamIsMe]

I always wondered why pi is used in it... I still don't know why but the video is cool

[@MathVisualProofs]

This relies on knowing that pi is defined in terms of the circumference and the radius of a circle: the circumference of the circle is 2pi*r. So then in this animation, the top half of the circle becomes the top of the rectangle and the bottom half of the circle becomes the bottom of the rectangle. Both these lengths are half the circumference, so they are pi*r.

[@SultanCAHAYAPUTRA]

I still dont get it how pi x r formed

[@MathVisualProofs]

It’s half the circumference.

[@michaelgyawu7929]

Charging by the way the circle was disassembled to create the circumference of the rectangle, shouldn't the area of that rectangle be : ((pi*r)/2))*r = (pi*r^2)/2. ?

[@MathVisualProofs]

The circumference of the circle is 2pi r. It splits to become the top and bottom lengths of rectangle. The sides are given by the radius of the circle. So the perimeter of the rectangle is 2r+2pi r. So the area is pi r r.

[@g9dhanushs161]

This isn't right it's wrong

[@Wutheheooooo]

what wrong?

[@thanhchan3365]

ISuch a helpful channel. I would repost your whole channel, without changing anything, on the nice platform named Gan Jing World. If you agree with that, please let me know. Many thanks!

[@MathVisualProofs]

I'm not sure why it's not enough to just have the content here? I am not sure I am ready to share it to other platforms that I am not yet familiar with. Thanks!