The 29-year-old Euler submitted the paper "Seven Bridges in Konigsberg", which solved this problem satisfactorily and created a new branch of mathematics-graph theory. He also published the paper "Solution to the Problem of Location Geometry", which expounded a problem and was the first model to apply graph theory and topology.
In this paper, Euler abstracted the problem of seven bridges, and regarded each land as a point, and the bridge connecting two lands was represented by a line. So as to obtain the geometric figure as shown in the figure. If we use four points A, B, C and D to represent the four regions of Konigsberg. In this way, the famous "seven bridges problem" is transformed into a question of whether these seven lines can be drawn with non-repetitive strokes.
If you can draw it, there must be an end point and a starting point in the figure, and the starting point and the end point should be the same. Because of symmetry, the effect is the same starting from b or c. If A is assumed to be the starting point and the ending point, there must be a starting line and a corresponding entering line. If we define the number of rows entering A as in-degree, the number of rows leaving A as out-degree, and the number of rows related to A as in-degree, then the out-degree and in-degree of A are equal.
That is to say, if there is a solution from A, then the degree of A should be even, but in fact the degree of A is 5 and odd, so we can see that there is no solution from A. At the same time, if we start from B or D, because the degrees of B and D are 3 and 3 respectively, they are all odd, that is to say, there is no solution from them.
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Leonhard Euler (1April 70715 ~1September 783 18) was a Swiss mathematician and natural scientist. 1707 was born in Basel, Switzerland on April 5, and 1783 died in St. Petersburg, Russia on September 8. Euler was born in a priest's family and was influenced by his father since childhood. /kloc entered university of basel at the age of 0/3, graduated from university at the age of 0/5, and obtained a master's degree at the age of 0/6.
Euler is one of the most outstanding figures in the field of mathematics in the18th century. He not only made contributions in the field of mathematics, but also pushed the whole mathematics into the field of physics. He is the most prolific mathematician in the history of mathematics, writing more than 800 pages of papers every year on average. He also wrote a large number of textbooks on mechanics, analysis, geometry and variational methods. Introduction to Differential Analysis, Principles of Differential Calculus and Principles of Integral Calculus have all become classic works in the field of mathematics.
Euler studied mathematics so extensively that important constants, formulas and theorems named after him can often be seen in many branches of mathematics. ? In addition, Euler also dabbled in architecture, ballistics, navigation and other fields. CharlesKleiber, Swiss Secretary of State for Education and Research, once said, "Without many scientific discoveries made by Euler, our life today would be completely different."
Laplace, a French mathematician, thinks that reading Euler is everyone's teacher. In 2007, in order to celebrate the 300th anniversary of Euler's birth, the Swiss government, the China Academy of Sciences and the Ministry of Education of China jointly held a commemorative event at the Documentation and Information Center of the China Academy of Sciences on the afternoon of April 23, 2007, reviewing Euler's life, work and influence on modern life. ?
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