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On 03/17/2008 08:40 AM, Dan MacIsaac wrote:
check out
http://xkcd.com/356/
and hints for elegant solutions are welcome (no, I don't have one).
Hint: Fourier transform.
Lurid details: http://www.geocities.com/frooha/grid/grid.html <http://www.geocities.com/frooha/grid/grid.html>
which cites
D. Atkinson and F.J. van Steenwijk.
"Infinite resistive lattices."
Am. Jour. Phys., 67 486-492 (1999).
BTW the Fourier idea is worth remembering, because it comes up
fairly often. Feynman uses it somewhere in volume II to calculate
the evenness of illumination at desk-height from an array of lights
at ceiling-height.
The take-home message is that Fourier methods are not limited to
waves. Any sort of periodicity will do, even if not wave-like.
Remember Fourier's book was _Théorie Analytique de la Chaleur_
and heat conduction is famously too overdamped to be wave-like.