Scaffolded Math and Science

(formerly ZeroSum Ruler)

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

Filed under: algebra,math education,number theory,proof — Shana Donohue @ 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.

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

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Does sphere + cone = cylinder?

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