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 [quote="Lepton"]This is beautiful. If you haven't before seen this construction for determining the volume of a sphere (assuming you know the volume of a cone and of a cylinder), try to figure out how it works. [url]http://www.its.caltech.edu/~mamikon/Sphere.html[/url] [spoiler]The blue line is the radius of the sphere, the green is the radius of the cone. The sum of the cross-sectional area at any particular height will be the sum of the squares of the lengths of these two lines, which is the length of the red line, by the Pythagorean theorem.[/spoiler][/quote]
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davidchatman
Posted: Tue Oct 25, 2011 9:54 am    Post subject: 1

That was impressive
Lepton
Posted: Mon Jan 31, 2011 4:50 pm    Post subject: 0

This is beautiful. If you haven't before seen this construction for determining the volume of a sphere (assuming you know the volume of a cone and of a cylinder), try to figure out how it works.

http://www.its.caltech.edu/~mamikon/Sphere.html

The blue line is the radius of the sphere, the green is the radius of the cone. The sum of the cross-sectional area at any particular height will be the sum of the squares of the lengths of these two lines, which is the length of the red line, by the Pythagorean theorem.

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