But why is a spheres surface area four times its shadow

The formula is no mere coincidence. Help fund future projects: An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: Discussion on Reddit: 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: ------------------ These animations are largely made using ma