1933? Hungarian mathematician George Sechris (George? Szekeres) is still only? 22? Years old. At that time, he often discussed mathematics with his friends in Budapest, Hungary. There is also a Hungarian-born math geek-erd?s· Parr (Paul? Erd？ S) great god. But at that time, Ordos only had? 20? Years old.
At a math party, a woman named Esther Klein (Esther? Klein) put forward the conclusion that if you draw five points on a plane (any three of which are not * * * lines), then there must be four points, and these four points form a convex quadrilateral. Szekeres and Erdos thought for a long time, but they didn't know how to prove it. So, this beautiful student proudly announced her proof that the convex hull of these five points (the smallest convex polygon covering the whole point set) can only be pentagon, quadrilateral and triangle. The first two cases need not be discussed, but for the third case, if two points in a triangle are connected into a straight line, then two of the three vertices of the triangle must be on the same side of the straight line, and these four points form a convex quadrilateral.
There are three positions of five points on the plane.
Everyone shouted brilliantly. After that, Erdos and Sai Keres were still obsessed with this problem, so they tried to popularize it. Finally, where are they? 1935? After publishing a paper, it successfully proved a stronger conclusion: for any positive integer? n？ ≥? 3. Is there always a positive integer? M, so as long as the points on the plane have? m？ A (and any three points are not * * * lines), then you must find a convex from it? n？ Edge shape. Ordos named this problem "Happy Ending Problem" (Happy? The ending? Question), because of this question, there is a spark between Jeangeorges Szekeres and Esther Klein, a beautiful classmate, getting closer and closer, and finally? 1937? Year? 6? Month? 13? I got married the same day.
Given? n？ , why don't you write down the minimum number of points required? Female (noun). Found? f(n)？ The exact value of is no small challenge. Because any three points on the plane can determine a triangle, so? f(3)？ =? 3? . Esther Klein's conclusion can be simply expressed as? f(4)？ =? 5? . Using some slightly complicated methods, we can prove it? f(5)？ Equal to? 9? . 2006? In, with the help of computers, people finally proved? f(6)？ =? 17。 For the bigger one? n，f(n)？ What are our values? ? f(n)？ Is there an accurate statement? This is one of the unsolved problems in mathematics. After decades, the problem of happy ending is still active in mathematics.
Anyway, the final outcome is really happy. Intimate after marriage? 70? During this year, they went to Shanghai and Adelaide successively, and finally settled in Sydney, and they never separated again. ? 2005? Year? 8? Month? 28? George and Esther died one after another, less than an hour apart.
? The story of Galois
Galois (évariste? Galois), 19? One of the greatest French mathematicians in this century, the only one I call a "genius mathematician". Him? 16? At the age of 18, I took the entrance examination for the Paris Institute of Technology. As a result, the examiner didn't know what to say because there were too many steps to solve the problem during the interview, and finally he failed the exam.
In the history of mathematics, Galois is undoubtedly the most legendary and romantic mathematician, and there is no "one". 18? /kloc-at the age of 0/8, galois beautifully solved the number one problem in mathematics at that time: why there was no general solution to polynomial equations of degree five or above. He submitted this research result to the French Academy of Sciences led by the great mathematician Cauchy? (Augustine Louis? Cauchy) is responsible for reviewing manuscripts; But Cauchy advised him to go back and polish it carefully (he always thought Cauchy had lost or hidden his paper, and the recent archives research of French Academy of Sciences only rehabilitated Cauchy). Later, Galois handed the paper to Fourier (Joseph? Fourier), but Fourier died a few days later, so the paper was lost. 183 1 year, galois submitted for the third time. The reviewer at that time was Poisson. He thought Galois's paper was difficult to understand and refused to publish it.
Because of some extreme political acts, Galois was arrested and imprisoned. Even in prison, he continued to develop his own mathematical theory. He met a doctor's daughter in prison and soon fell in love. But the good times didn't last long, and their feelings soon broke down. The second month after his release from prison, Galois decided to fight for his beloved girl and one of her political opponents. Unfortunately, he was shot and died in the hospital the next day. Galois's last words were to his brother Alfred: "Don't cry, I need enough courage? 20? /kloc-died at the age of 0/8. "
As if he had a premonition of his own death, the night before the duel, Galois stayed up all night, wrote down all his mathematical thoughts and gave them to him together with three manuscripts? He met his good friend Chevalier. At the end of the letter, Galois left a will, hoping that Sheva could give the manuscript to two great German mathematicians at that time (Karl? Gustav. Jacob. Jacoby) and Gauss (Karl? Friedrich? Gauss), let them publicly express their views on these mathematical theorems, and let more people realize the importance of this mathematical theory.
Chevalier followed Galois's wishes and sent the manuscript to jacoby and Gauss, but they didn't receive any reply. Until? 1843? Mathematician Joseph liouville (Joseph? Liouville) only confirmed Galois's research results and published them in Journal of Pure and Applied Mathematics (Journal? De? Math? Pure? et？ Decals). People summarized Galois' whole set of mathematical thoughts as "Galois Theory". Galois made a unique analysis of the structure of solutions of algebraic equations by using group theory. A series of algebraic equations such as the impossibility of solving roots and straightedge can be solved by Galois theory, and concise and perfect solutions can be obtained. Galois theory played a decisive role in the development of algebra in the future.
Descartes' story
Descartes (Rene? Descartes), 17? In the 20th century, the famous French philosopher once put forward the philosophical viewpoint of "I think, therefore I am", and Descartes, who has the title of "father of modern philosophy", also made great contributions to mathematics. The plane rectangular coordinate system that everyone learned in middle school is called Cartesian coordinate system.
It is said that Descartes once went to Sweden and met the beautiful Swedish princess Christina. Descartes found Princess Christina clever and did it? The princess's math teacher? So they are completely immersed in the world of mathematics. When the king learned about this, he thought Descartes was not good enough for his daughter. Not only did he forcibly separate them, but he didn't receive all the letters Descartes wrote to the princess. Later Descartes contracted the Black Death and sent the last letter to the princess before he died. There is only one line in the letter: r=a( 1-sinθ).
The king and ministers naturally didn't understand what this meant, so they had to return it to the princess. The princess established a polar coordinate system on paper, traced the points of the equation on it with a pen, and finally solved the secret of this line-this is the beautiful heart line. It seems that mathematicians have their own romantic ways.
A= 1
In fact, Descartes and Christina did have a friendship. But what is Descartes? 1649? Year? 10? Month? 4? I came to Sweden at the invitation of Christina, who had already become Queen Christina. And Descartes and Christina are mainly talking about philosophical issues. It is recorded that Descartes can only discuss philosophy with Queen Christina at five o'clock in the morning because of her tight schedule. Cold weather and overwork made Descartes unfortunately suffer from pneumonia, which is the real cause of Descartes' death.
Whether the story of the heart line is true or not is left to everyone to judge for themselves.