欧拉引入多面体公式的动因探析

Some Analyses on the Motivation of Introduced Polyhedron Formula by Euler

欧拉在1750年提出的多面体公式,标志着几何向拓扑的过渡,与之相关的欧拉示性数是当代数学中的一个重要概念。欧拉类比平面几何来认识多面体,观察到多面体的本质——顶点数、棱数和面数之间的关系。在欧拉之前,希腊人、开普勒和笛卡尔对多面体理论做过一定的研究。通过对比开普勒、笛卡尔和欧拉关于多面体理论的工作,从原始文献出发剖析欧拉引入多面体公式的动因,进而更好地理解欧拉多面体公式的拓扑意义。

The polyhedral formula introduced by Euler in 1750 marked the transition from geometry to topology,and the related Euler characteristic is an important concept in contemporary mathematics.Euler understood polyhedron by analogy with plane geometry,and observed the essence of polyhedron—the relationship between vertices number,edges number and faces number.Before Euler,the Greeks,Kepler and Descartes have done some research on polyhedron theory.By comparing the work of Kepler,Descartes and Euler on polyhedron theory,the author of this paper dissects the motivation for Euler introduction of the polyhedral formulation from the original literature,and thus better understands the topological significance of Euler polyhedral formulation.