Unraveling a circle area

In this short, we show a fascinating method of determining the area of a circle using the "method of exhaustion.”

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.

If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualPr.... Thanks!

Here are other versions from me:
   • Circle Area by Peeling Circumference  
   • Circle area from peeling circumferences (p...  

To see an alternate (and quite viral) video showing this in stop motion, check out this one from @MinutePhysics :    • Proof Without Words: The Circle  

For more information about this construction, see
https://personal.math.ubc.ca/~cass/co...

or check out this nice survey article by David Richeson from the May 2015 issue of The College Math Journal: https://doi.org/10.4169/college.math.... .

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

To learn more about animating with manim, check out:
https://manim.community