• Analysis of Four Color Theorem Based on Polynomial-Circular Logarithmic Equation

    Wang Hongxuan1, Zhou Yiyi2, Wang Yiping3

    1. Jiangshan Experimental High School, Zhejiang Province, Zhangzhou 324100, China.
    2. No. 2 Middle School, Shengzhou, Zhejiang Province, Zhangzhou 324000.
    3. Quzhou City, Senior Engineer Engaged in Mathematics and Power Engineering Research and Teaching Zhejiang Quzhou 324000.


    The four-color theorem, also known as the four-color conjecture and the four-color problem, is one of the three major mathematical problems in the modern world. The Four color theorem was proposed by a British college student named Goodrich Francis Guthrie in the map coloring. Augustus De Morgan (1806-1871) A letter to Hamilton on October 23, 1852, provided the most original account of the source of the four-color theorem. For a century and a half, in order to prove this theorem, mathematicians are closely related to contemporary mathematical combination, graph theory, topology, generalization, fractal, collection, and computer computing foundation. The concepts and methods introduced are stimulated. The growth and development of topology and graph theory.

    In 1975, Bemanh-Hartmanis conjectured that there is a pair of G(•) and F(•) reciprocal. If the proof is true, then the polynomial time can be calculated, with polynomial time isomorphism [1].

    In 1983, Chinese mathematician Xu Lizhi said in the “Selection of Mathematical Methodology” that the main point of calculus polynomial is continuous regularization[2]. If anyone can make a very useful relationship structure (S), it is very useful to introduce it, and G(•) and F(•) can perform important inversions [3].

    The four-color theorem lies in the sufficiency, necessity, and uniqueness proof of the infinite non-repetition of the “four-four combination” under the infinite block. Most mathematicians think that relying on the existing traditional mathematics system can’t solve it, at least it is very difficult. In 1976 and 1994, American mathematicians K. Appel and W. Haken announced the use of electronic computers to obtain the proof of the four-color theorem; through the computer, after 100 billion power (power dimension) calculation.

    Mathematicians expect traditional simple mathematical proofs. In this paper, we propose that “any four-color non-repetitive combination of spliced tiles, plus a final closed curve” becomes a polynomial, converted into “abstract circular logarithmic equation without specific element (color) content, and arithmetic four operations. Number (relativistic construction). Conveniently prove the four-color theorem, replacing the 1976 American computer with 10 billion calculations.

    I hope this article can provide useful help to relevant scholars, teachers and seniors at home and abroad. If you are not good, please criticize and teach, and welcome exchanges and cooperation.

    Keywords: high-order multivariable polynomial, four-color theorem, combination coefficient, average of block, round logarithm

    Pages: 361 – 377 | Full PDF Paper