Do you know Leonardo da Vinci's circle area proof?

Happy Pi Day! Sato Moshun and Leonardo da Vinci independently devised an incredible visualization to find the formula for a circle's area. #Shorts

(Apologies there was no early access on Patreon--I finished making the video just in time for Pi Day).

Wikipedia
Cut The Knot area of a circle
Area of a circle, formula explained (mathematicsonline)
Understanding the Formula for Area of a Circle #shorts (mathematicsonline)

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[mrmimeisfunny]

I like how all these neat proofs of the area of a circle come extremely close to calculus.

I'm now wondering if there is a proof that isn't based on calculus.

[Cookiedon]

This is a great way to explain integrals in calculus

[TheLaw-mhpb]

Wow so not only is he a great actor, he's also a mathematical genius...

[punisherlee]

If many were taught this instead of being told "That is just the formula", they would've loved mathematics

[muhammadaryasaputra]

If you ask "where does π come from?" or "where does the formula of the circumference came from?", great question. The answer is

π is *defined* as circumference/diameter

[bwcbiz]

A very interesting precursor to integral calculus. If only they'd thought to apply this technique in other "areas".

[jackbrady]

SOOOO COOL. I WISH THEY SHOWED ME THOS AT SCHOOL

[nickkings]

There is atleast a couple different ways you can come to that same conclusion and the fact that this is how they did shows some creativity and outside the box thinking.

[vitalsbat]

this is how i learnt the circle's area

[logan_e]

Cool, I knew it worked but not exactly why until now!
Thank you.

[ghzich]

How did they knows da vinci found this formula?

[kira]

I think the value that we get by pi r² isn't 100% accurate as an arc of a circle can never be straight no matter how thin we slice it. Just like the value of pi, we can never accurately measure its area, we can just get infinitely closer to it. (pls let me know if I'm wrong tho)
EDIT- These small inaccuracy becomes heavily considerable when it comes to deal with the big circles out there in space

[SnakeWasRight]

The circle is now complete. When I left you, I was but the learner, now I am the master.

[chuckmckee]

I sent my son to college to learn math. I was so proud when he got home. I had all the relatives over. I ask him to say something he learned. He’s said pie r squared . I was so disappointed. I said boy, everybody knows pie r round . Lol 😂

[context]

All that circular power in my hairbrush…

[sbeve]

Da Vinci: Okay so here's how you find the area of a circle...

Everyone else: ITS ENOUGH SLICES

[Kweesh]

On the contrary, this is probably one of the most credible things I've ever heard.

[Ryniano]

I feel like math would be so much more enjoyable if they taught it like this, almost like history

[GreenFesh]

I feel this approach is a little misleading as you have to be careful when it can actually be applied. The circumference of a circle is 2*pi*r. So with a radius of 0, 5 the circumference is pi. Now imagine a square around this circle touching the circle on four sides (tangent). The square would have the side length 1 and thus a circumference of 4. Now create for squares that fit into the four corners of the first square and touch the circle with one corner, they must be the maximum size possible. Cut them out. The circumference of the square remains 4, but the area has shrunk. Now create 8 maximal sized squares into the 8 corners and cut them out again. Repeat this process infinitely, so that the circumference of the square wraps all around the circle. There you have it, the circumference of the circle is 4 thus pi=4.

The flaw here is that no matter how small it gets or how much you zoom in, the outline of the square will always have a longer path to go than the circle. It doesn't matter that you go infinitely small, because the angle that the square goes doesn't change. I feel like this issue gets overlooked sometimes in these kind of proofs that we see in the video. So why is this not an issue here? I mean, no matter how infinitely small you get, the outline of a circle will never be the same as a straight line. What am I overlooking here?

[Stuffinround]

“Ooh a pi, save me a slice. Okay that, that’s good, it ITS ENOUGH SLICES”