Graph Theory: The Four Coloring Theorem

Graph theory: The four tinting theorems "All flat maps can be colored four colors" seem to be very basic and easy to prove. However, this simple concept took over 100 years, involving more than a dozen digital technicians. For centuries many people have thought about this idea and have created many other problems, solutions, and mathematical concepts. I thought the Four Coloring theorem is very interesting. It is because it is necessary to prove its obvious simplicity and its long and difficult struggle.

The four color theorem shows that a plan view (or similarly, a plan view of a two-dimensional region such as a country) can be colored using four colors so that adjacent vertices (or regions) are always different colors ing. Usually three colors are not enough to guarantee this. The largest flat full graph has four vertices. The number of rows representing 1, 2, and 3 is the same as the number displayed. Brahmin Indians simplified by connecting their four lines to the cross that looks like a modern plus. Shunga adds a horizontal line above the number, and Kshatrapa and Pallava change the number to the point where writing speed is a secondary problem. Arabs 4 still have the initial concept of the cross, but for efficiency, they are made by connecting the "west" end to the "north" end; the "east" end ends with a curve

The history of discrete mathematics contains many challenging problems that are drawing much attention in this area. In graph theory, the motivation of many studies is to try to prove the four color theorem first mentioned in 1852, but it was not proved until 1976 (massive computer aid is based on Kenneth Appel and Wolfgang Haken It was used by). Logically, the second problem in the list of unresolved issues proposed by David Hilbert in 1900 was to prove that arithmetic axioms are consistent. The second incompleteness theorem that Gödel proved in 1931 shows that this is impossible - at least not with arithmetic itself. Hilbert's tenth question is to determine whether a given polynomial Diophantine equation with integer coefficients has an integer solution. In 1970, Yuri Matiyasevich proved that this could not be done.

Theorem is the most important result of all elementary school mathematics. It is the driving force of many advanced mathematics like Fermat's last theorem and Hilbert space theory. Pythagorean theorem states that in the case of a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. There are many ways to prove Pythagorean theorem. A particularly simple one is a scaling relationship resembling a numerical domain. Does Pythagoras draw Pythagorean theorem or summarize it by studying ancient culture; Egypt, Mesopotamia, India, and China? What do these ancient cultures know about this theorem? Where is the theorem used in their society? In the book "geometry and algebra in ancient civilization", the author argues about the person who originally led the Pythagorean theorem.