Infinite Resistor Grid
On an infinite grid of one Ohm resisters what is the
resistance between two nodes one knights move away? My friend asked
me this question and I had no idea, so I asked my AP Physics
teacher. He did not have an answer either so I turn to the plethora
of knowledge that is the Internet.
This is a classic problem in physics (it has its own *cartoon*!), so rather
than repeat the solution here, I shall refer you to one of several solutions
easily found through almighty Google:
Incidentally, may I suggest you seek revenge on your friend by asking
him/her to calculate the same resistance, but for a 3D grid. You may find
this useful in judging the response: http://arxiv.org/abs/cond-mat/9909120
Other references of note:
Look out for trucks!
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Update: June 2012