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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