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Ptolemy, the great misunderstood scientist. Reviled for overcomplicating the equations of motion by requiring that celestial motion be composed of combinations of circles upon circles, rather than the more straightforward ellipse.

However, Fourier Analysis, one of the hottest methods to hit the physics scene does just this...

Ptolemy was years before his time re: analysis, even if his physical intuition was a bit off.

I'm Probably about 5d AGA, 3d KGS/IGS (I'm so close to 3d KGS that it should happen in the next couple days), The 2006 Dote Memorial tournament in SF will be my first tournament, though, so we'll see how it turns out.

UPDATE: 3rd in 2006 Dote Memorial Tournament Dan Division

Santa Cruz Go club Member: (If you're in the area we play at Cafe Pergolessi (Corner of Cedar and Elm) on Thursdays from 7:30 till closing.

KGS Clan Member: PStyle

ilan: Though you are basically correct, Ptolemy was criticised by Copernicus for abandoning epicycles in favour of the equant, which is an approximation of the ellipse. It appears that Copernicus constructed his heliocentric theory in order to rehabilitate epicycles and by using them, his model was actually more complicated (used more epicycles) and was less accurate. Also, epicycles are not strictly Fourier analysis, because the frequencies do not have to be rationally related. In fact, it is what is now called almost periodic functions. The real irony in the criticism you state is that in order to locate an object in its elliptical orbit, you have to solve Kepler's equation, which cannot be done explicitly, and the best method (developed by Bessel who invented his functions for this) is to use Fourier series, which are epicycles as you state, in fact an infinite number.

ptolemy last edited by Phelan on November 14, 2006 - 00:21
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