If I recall correctly, for the resistance between diagonal points, one might need Fourier series, but there is a simple method for nearest lattice points. -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Eugene Salamin Sent: Friday, January 28, 2011 10:06 AM To: math-fun Subject: Re: [math-fun] The people you know... For the complete graph with n vertices, with 1 ohm edges, place 1 volt across two vertices. The situation is symmetrical under permutation of the remaining n-2 vertices, and under exchange of the 2 vertices with reversing the sign of the currents. So the n-2 vertices are at 1/2 volt. Then the current into the 1 volt vertex is (1 + (n-2)/2) = n/2 amps, and thus the resistance is 2/n ohms. The square lattice problem was discussed on math-fun some time ago, and a solution was presented by means of Fourier series. -- Gene ________________________________ From: "Cordwell, William R" <wrcordw@sandia.gov> To: math-fun <math-fun@mailman.xmission.com> Sent: Fri, January 28, 2011 8:51:57 AM Subject: Re: [math-fun] The people you know... There's a nice physics problem about the equivalent resistance between two nearest points, if one is considering an infinite square lattice with 1 ohm resisters between nearest points. -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Adam P. Goucher Sent: Friday, January 28, 2011 9:49 AM To: math-fun Subject: Re: [math-fun] The people you know... I can't resist posing the following question: "Connect two people with a one-ohm resistor if they mutually know each other. What is the mean resistance between each pair of people?" You could, as Mike Stay suggested, replace this problem with an analogous one about a given social network. Sincerely, Adam P. Goucher _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun