Scaffolded Math and Science

(formerly ZeroSum Ruler)

Archimedes says “cone + sphere = cylinder”? April 14, 2012

Filed under: algebra,math education,number theory,proof — Scaffolded Math @ 5:19 pm
Tags: ,

Archimedes of Syracuse (87 BC – 212 BC), before the eternal time sucks of Facebook and DrawSomething, sat and imagined a cone and a sphere balancing one side of a scale, and on the other side balancing against these two objects was a cylinder.  The sphere he imagined has the same diameter as height of the cylinder and the cone and he reasoned that the scale would remain perfectly balanced.

 

But would it?  Using just their volume formulas, which Archimedes did not yet have, can we see that this works? 

Does sphere + cone = cylinder?

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