Watch this watery proof for the volume of a sphere. Courtesy of Archimedes and @mikeandallie. Key shot at 1:30https://m.youtube.com/watch?time_continue=43&v=QNsLnWB6fV4 …
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Replying to @stevenstrogatz @mikeandallie
Follows from the fact that the area of a hemisphere of radius r is equal to the area of a cylinder of radius and height r.
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Archimedes' first theorem of symplectic geometry. Elegant and profound, like all his work.
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Replying to @MathPrinceps @agolian and
Perhaps worth remarking that the fascinating and mysterious Kevin Brown offers a "minimal calculus" proof: http://bit.ly/2w8nms7
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