四色问题的直观几何论证及单纯性地图四色定理

对地图染色问题的论证已困扰学术界160 余年，根本原因在于它不是经典数学问题，而人们总想用经典数学方法去证明它。用直观几何方法将其转换为染色等价的正规地图，并严格证明“相邻域定理”；建立并分析最小单元地图的染色，发现了单纯性和关联性两种地图染色模式；建立基本单元地图模型，创造由基本单元地图模型成长为地图的过程与染色相结合的直观方法；严格证明四色定理：任何单纯性地图可以至多用4 种颜色染色，而任何关联性地图所需颜色数目不确定；创造“缩灭法则”去简化复杂地图；举出了《中国行政区划正规地图》应用实例。

Visualized Geometrical Demonstration of the Four Colors Problem and theFour Color Theorem of Simple Map

The arguments of the least colors that should be used to dye the 2D net color blockgraph, such as maps and patterns, have puzzled the academia for one hundred and sixty years ormore. The basic reason is that the scholars have been working on to solve the problem withclassical mathematics methods, even though it is not a classical mathematics problem. Visualizedengineering geometry is used to turn the 2D net color block graph into dyeing equivalence normalmap, and critically adjacent domain axioms proved. The smallest unit of maps and their dyeingmode is also established. Two kinds of map dyeing mode are found in the process. The first issimple dyeing mode, and the second is the relevant dyeing mode. At the same time, a visualizedmethod is developed combining the dyeing and the process of turning the smallest map unit intomaps together. It is proven critically that any simple maps are suitable for the least four colorsdyeing method, but for the relevant maps, the number of colors that should be used are uncertain.