Analytical proof on four color guess and mapping application(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....
Main Authors: | LIUQing-min(刘庆民), OUYANGFu(欧阳富), CAIHan-zhong(蔡汉忠) |
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Format: | Article |
Language: | zho |
Published: |
Zhejiang University Press
2011-07-01
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Series: | Zhejiang Daxue xuebao. Lixue ban |
Subjects: | |
Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2011.04.001 |
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