关联电阻网络的一些三角恒等式  

Some Trigonometric Identities Associated with the Resistance Network

作　　者：谭志中[1] 

机构地区：[1]南通大学理学院,江苏南通226007

出　　处：《南通大学学报（自然科学版）》2013年第1期87-94,共8页Journal of Nantong University(Natural Science Edition)　

基　　金：南通大学自然科学基金项目(11Z054);南通大学教学研究项目(2011B06)

摘　　要：从电阻网络等效电阻的研究出发,解决了一些相关联的数学问题.采用变换与构造的方法,建立并证明了与电阻网络问题相关的6个三角恒等式以及6组恒等式推论,并进一步提出了一个恒等式猜想.Research in the equivalent resistance formula for any m^n-resistor network is always a difficult problem of science, among which, derivation of the universal formula of equivalent resistance involves establishment and proof of some trigonometric identities. In the actual need of our study in the equivalent resistance of resistance network, in this paper, six related trigonometric identities together with six corollaries set are established and proved. The main methods of proof are transformation and structure, meanwhile, an identity conjecture is put forward at the end of this paper.

关 键 词：电阻网络 等效电阻 三角恒等式 猜想 

分 类 号：O124[理学—数学] O44[理学—基础数学]