Guest Posted February 28, 2011 Report Share Posted February 28, 2011 consider and infinite plane with each lattice point connected to the four adjacent lattice points by a 1 ohm resistor. What is the resistance between the points (0,0) and (2,1)? Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted March 1, 2011 Report Share Posted March 1, 2011 (8-π)/(2π) Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 1, 2011 Report Share Posted March 1, 2011 (8-π)/(2π) that seems to be correct, but would you mind explaining why? Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted March 1, 2011 Report Share Posted March 1, 2011 that seems to be correct, but would you mind explaining why? Sorry, it would take me far too long to write out a cogent explanation. I used a Linear Algebra approach although there are many others (Fourier Analysis being one of them). I can't see any way to explain it simply. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 1, 2011 Report Share Posted March 1, 2011 Sorry, it would take me far too long to write out a cogent explanation. I used a Linear Algebra approach although there are many others (Fourier Analysis being one of them). I can't see any way to explain it simply. That's fair. I used an infinite series of infinite series of infinite series... I gave up on evaluating them exactly, but by approximating them, got an answer very close to yours. Luckily for me, I just started an online linear algebra course, so hopefully I'll be able to do that too pretty soon...maybe... Thanks again and nice work! Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 1, 2011 Report Share Posted March 1, 2011 Warning: these problems involve some risk. Having said that, here are more values. Quote Link to comment Share on other sites More sharing options...
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consider and infinite plane with each lattice point connected to the four adjacent lattice points by a 1 ohm resistor. What is the resistance between the points (0,0) and (2,1)?
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