关键词: 6×n阶矩形网络, 证明猜想, 等效电阻, 差分方程, 矩阵变换, 三角恒等式

Abstract: Study on equivalent resistance formula of any k×n-resistor netwok is a scientific problem, so far people have educed the equivalent resistance formula in the five cases that k = 1,2,… ,5. But it is only given as a conjecture for the universal formula of equivalent resistance when k ≥6. Based on the established method of the ex- isting achievements which studied equivalent resistance of any k×n resistor network, we prove the corretness of conjecture of the equivalent resistance formula when k = 6, and give the formula of the equivalent resisance of the infinite network. We obtain some new trigonometric identities when the result is compared with others.

Key words: 6×n-rectangular network, a proof of conjecture, equivalent resistance, difference equation, matrix transform, trigonometric identity