Wednesday, October 15, 2008

This is so nerdy...

So my daughters (or maybe one of them?) got me a T-shirt that says "enjoys calculus" which I'm afraid I've just demonstrated in wikipedia's article on "Volume" -- particularly in the derivation for the formula for the volume of a sphere.

Here's how it happened. I was thinking about spheres for some reason, and I couldn't remember how to calculate the volume of a sphere. In fact I couldn't remember how to calculate the surface area either. I mean, one could look up the formulas somewhere, but how can you derive the formulas?

I couldn't think of any way to get any of them other than through calculus -- integrating the area of circular "slabs" parallel to the x-y plane as you take z from 0→R, which yields 4πR3.

Anyway, the lack of a non-calculus derivation bothered me because it seemed to me that when we learned this stuff in geometry class, we didn't know any calculus. H'm... On the other hand, maybe it was like, you know, the centripetal force formula mv2/R, which we just memorized in high-school physics but turns out to be derivable by parameterizing (x,y) in terms of t....

Judy suggested that I google on "volume of a sphere" and see what other calculation methods might be out there... didn't find anything easier than the first method on wikipedia's "Volume" article. That's when I noticed that the previous version had a gap... there was this weird "(This substitution is difficult to" in it, immediately followed by "Thus, the sphere..."

So I put something there I thought easier to follow. Oddly, the page was vandalized within 15 minutes... fixed immediately.

off-white and nerdy....

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