Proof and extension of the resistance formula for an m x n cobweb network conjectured by Tan, Zhou and Yang

J. W. Essam; Zhi-Zhong Tan; F. Y. Wu

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arXiv · 1312.6727

Proof and extension of the resistance formula for an m x n cobweb network conjectured by Tan, Zhou and Yang

J. W. Essam·Zhi-Zhong Tan·F. Y. Wu

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Abstract

An m x n cobweb network consists of n radial lines emanating from a center and connected by $m$ concentric n-sided polygons. A conjecture of Tan, Zhou and Yang for the resistance from center to perimeter of the cobweb is proved by extending the method used by the above authors to derive formulae for m = 1, 2 and 3 and general n. The resistance of an m x (s+t+1) fan network from the apex to a point on the boundary distant s from the corner is also found.

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J. W. Essam, Zhi-Zhong Tan, F. Y. Wu. 2013-12-24. Proof and extension of the resistance formula for an m x n cobweb network conjectured by Tan, Zhou and Yang. https://arxiv.org/abs/1312.6727

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