Visual math every student should see - circle area unwrapping

Happy Pi Day! In the 12th century, Rabbi Abraham bar Hiyya discovered a stunning visualization of a circle's area. #shorts

Area of a Circle by Rabbi Abraham bar Hiyya Hanasi
Area of a Circle by Rabbi Abraham bar Hiyya Hanasi
David Garber and Boaz Tsaban, A mechanical derivation of the area of the sphere, The American Mathematical Monthly 108 (2001), 10--15.
Wikipedia

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[SlimThrull]

Sounds like he invented integrals long before Newton did.

[Mansory]

Thanks, something this simple like a short Video of 10 seconds can help you understand a topic much better.

[cguy]

I have NEVER seen this before. Brilliant. I can only imagine that the proof was ridiculously complex, it always seems that way when you have something this intuitive, simple, and elegant.

[praveenraj]

I had this doubt for a very long time, thanks for resolving it.

[UltraLightSP]

Yep, similar concept covered in 3b1b's Essence of Calculus series. And this really is a wonderfull representation of what calculus is.

[henrytang]

This is even better than the rectangle visualisation.

[chevyDboyMike]

I had heard or read that a circle is constructed of tiny line segments. This really shows how its true.

[XJWill]

Now give a similarly simple demonstration for why the circumference is 2 pi r, which was used as an assumption for that "demonstration".

[IS-pydk]

Happy Pi Day Every american 😀
Asians, please wait till 22nd July or 22 - 7 - 2022 😅

[claudreindl]

You can do the same equivalent thing using 1/4 of a circle. The circular length is 2•pi•r/4. Make infinitely small slices that vary in length from 0 to r. The average is r/2. (2•pi•r/4) •(r/2) •4 quadrants is pi•r^2.

[mmehul]

Aryabhata, the great Indian mathematician, has written this method to find area of circle in his book Aryabhatiya some 1500 years back.

[SogehtMathe]

Why haven't I seen this before? This is amazing!

[maxgolder]

I’ve read about this guy in gemara but never heard of this

[TheChamp]

Now do one for Surface Area = 4pi x r²

[zxlittlexzexchernyap]

Ah yes, a 10 sec shorts video casually killing a forty minute math lesson🤣

[nanananana]

I just left a comment on your other video about this method!!! This one is my favorite ♥️

[muhammadaryasaputra]

For anyone curious why the circumference of circle is 2πr?

Because π is *defined* as circumference/diameter.

We can't prove a definition

[KingGisInDaHouse]

Or the old fashioned way of cutting up into pizza slices to approximate a parrelelogram

[danburch]

Seems like that approach can also be used to find the surface area of a sphere (=4π²) or the volume of a sphere (=1.333π³). That would be interesting to see.

[Umbra]

This also works in three dimensions! If you take a sphere and peel off its surface, you can shape it into a circle with the area 4*pi*r^2, as per the definition of the sphere's lateral surface. Repeatedly doing this with infinitesimally small peels, you get a cone with base 4*pi*r^2 and height r. Following the formula for the volume of the cone, we get 4*pi*r^3 / 3, which is exactly the volume of the sphere!