In this short, we show two fascinating methods of determining the area of a circle using the "method of exhaustion." Which one do you like better?
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The top animation unrolls 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.
Here are other versions from me:
• Circle Area by Peeling...
• Circle area from peeli...
To see an alternate (and quite viral) video showing this in stop motion, check out this one from @MinutePhysics : • Proof Without Words: T...
For more information about this construction, see
personal.math....
or check out this nice survey article by David Richeson from the May 2015 issue of The College Math Journal: doi.org/10.416... .
This bottom 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.
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/de..., page 130-132 and Beckmann, Petr (1976), A History of Pi, St. Martin's Griffin, page 19).
Here are other versions from me:
• Circle Area (classic v...
• Circle Area Derivation...
You can also read more about this in a great NYT article by Steven Strogatz: archive.nytime...
#math #manim #visualproof #proofwithoutwords #circle #circlearea #archimedes #radius #area #areaofcircle #pi #piday #shorts #circle #archimedes #infinite #methodofexhaustion
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