四色猜想的解析论证及其在地图绘制中的应用

依据欧拉定理，研究了边数差和着色数计算公式，对四色猜想进行了研究．借助四面体顶点数与面积数相等的原则、多面体边数不变的原则和多余理论，用边数差数学计算方法论证了四色猜想．用简单的数学公式和几何作图方法说明了四色猜想的合理性，为其提供了可靠的理论依据．用“三色包点”和“以面切体”的几何作图法，证明多面体和平面地图的着色数恒为4；非三色包点的图形，可以通过“以面切体”的方法转换成三色包点的图形；使用多余国家、多余边数的数学技巧代替计算机使用的不可避免性、可约性是合适的．理论分析及实例论证表明该方法简单可行．

Analytical proof on four color guess and mapping application.

Developed formulae of edge difference and coloring number,discussed four color guess by the Euler theorem.By the aid of the principle that acme number of tetrahedron is equal to its area number,and edge number is changeless,as well as superabundance theoery,demonstrated four color guess by edge difference method.Explained the rationality of four-color guess by mathematics formula and simple geometry method,and offered the reliable theoretical foundation for it.Colord numbers of polyhedron and plane map iden...