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From: Loyd <Loydlin@aol.com> To: Teacher2Teacher Public Discussion Date: 2003101112:20:53 Subject: Re: Volume formula for a sphere; Archimedes Watched NOVA a week or so ago about a lost text of Archimedes. He was the most proud of the fact that he discovered that the ratio of a sphere to a cylinder is exactly 2/3. That is if the sphere diameter is the same as the height and diameter of the cylinder, the ratio holds. Divide 4/3 x pi x r^3 by Pi x r^2 x 2r (diameter = 2r) The ratio becomes: (4/3)/(2)=2/3 (all the r's and pi's cancel.) This was amazing to me since I had never heard this. I suppose it is old "hat" to other teachers although I looked in several geometry texts and found no reference to that problem. Archimedes wanted his grave stone to have engraved on it, a sphere resting on top of the cylinder. What the show didn't make clear is whether the 2/3 rule was in the lost text or was discovered earlier in texts that weren't lost.
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