But why is a sphere’s surface area four times its shadow?
The formula is no mere coincidence.
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The first proof goes back to Greek times, due to Archimedes, who was charmed by the fact that a sphere has 2/3 the volume of a cylinder encompassing it, and 2/3 the surface area as well (if you consider the caps). Check out this video for another beautiful animation of that first proof:
Calculus series:
Thanks to these folks for letting me use their images at the end:
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These animations are largely made using ma
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