Definition:

Seva's theorem means that if you take any point o in △ABC and extend the intersection of AO, BO and CO to d, e and f respectively, then (BD/DC )× (CE/EA )× (AF/FB) =1.

Four-color theorem: also known as four-color conjecture and four-color problem, is one of the three major mathematical conjectures in the world. Its content is: a map only needs four colors to mark.

Ten-color theorem is also called Heawood theorem. In the process of trying to prove the four-color theorem, human beings find it easier to draw and construct the 10 plane with connected areas on the surface.

Put forward the four-color theorem problem;

1852, when guthrie, who graduated from London University, came to a scientific research unit to do map coloring, he found that each map could only be colored in four colors. Can this phenomenon be strictly proved by mathematical methods?

He and his younger brother are determined to give it a try, but the manuscript paper has been piled up, but the research work has made no progress.

1852, 10 year123 October, his younger brother asked his teacher, the famous mathematician de Morgan, for proof of this problem. Morgan couldn't find a solution to this problem either, so he wrote to his good friend, Sir Hamilton, a famous mathematician, for advice.

But until the death of 1865 Hamilton, this problem was not solved.

1872, Kelly, the most famous mathematician in Britain at that time, formally put forward this question to the London Mathematical Society, so the four-color conjecture became the focus of the world's mathematics community, and many first-class mathematicians in the world participated in the conference war of the four-color conjecture one after another.

Since then, this problem has spread among some people. At that time, the harmony between the angle bisection and the square was "notorious" in society, and the "four-color plague" had quietly spread.

affect

Mathematicians have racked their brains to prove this theorem, and the introduced concepts and methods have stimulated the growth and development of topology and graph theory.

In the research process of "four-color problem", many new mathematical theories have emerged and many mathematical calculation skills have been developed. For example, turning the coloring problem of maps into a graph theory problem enriches the content of graph theory.

Moreover, the "four-color problem" has also played a role in effectively designing airline flight schedules and designing computer coding programs.