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teflonian · 10-07-2003, 10:32 AM

Ok... I am too far removed from calculus to fire this one up and figure it out really quickly, but I imagine there are a couple of things I can add to this discussion...

First off, you can make a 3-d object from a line. Just imagine taking a string covered in paint, holding one end, and smearing it around in a circle on a piece of paper (2-d now). Now take that 2-d paper and bend it in any sort of three dimensional shape... This isn't taking a 1-d object and magically transforming it to a 3-d shape.. Rather it is just describing the way to generate a 3-d shape from a mathmatical 1-d function.

And, to get to your question TheClarkster, I don't really remember how to find x-bar, etc, but do recall there being equations for these sorts of things... But I figure that one or two of the averages are going to be at the axis of rotation (so, at x=0 or y=0 or z=0)... As there would be equal "mass" of the line on all sides of the axis of rotation...

Hope... somebody else can be of more help...

10-07-2003, 10:32 AM	#8 (permalink)
teflonian Appreciative Location: Paradise	Ok... I am too far removed from calculus to fire this one up and figure it out really quickly, but I imagine there are a couple of things I can add to this discussion... First off, you can make a 3-d object from a line. Just imagine taking a string covered in paint, holding one end, and smearing it around in a circle on a piece of paper (2-d now). Now take that 2-d paper and bend it in any sort of three dimensional shape... This isn't taking a 1-d object and magically transforming it to a 3-d shape.. Rather it is just describing the way to generate a 3-d shape from a mathmatical 1-d function. And, to get to your question TheClarkster, I don't really remember how to find x-bar, etc, but do recall there being equations for these sorts of things... But I figure that one or two of the averages are going to be at the axis of rotation (so, at x=0 or y=0 or z=0)... As there would be equal "mass" of the line on all sides of the axis of rotation... Hope... somebody else can be of more help...