This leads to the problem of stroke.
2. One of the famous classical mathematical problems. In a park in Konigsberg, there are seven bridges connecting two islands and islands in the Fritz fritz pregl River with the river bank (pictured). Is it possible to start from any of these four places, cross each bridge only once, and then return to the starting point? Euler studied and solved this problem in 1736. He simplified the problem to the "one stroke" problem shown on the right, which proved that the above method was impossible.
Hot issues in graph theory research. 65438+ K? nigsberg, Prussia. At the beginning of the 8th century, the Fritz fritz pregl River passed through this town. Naif Island is located in the river, and there are 7 bridges on the river, connecting the whole town. Local residents are keen on a difficult problem: is there a route that can cross seven bridges without repetition? This is the problem of the seventh bridge in Konigsberg. L. Euler uses points to represent islands and land, and the connecting line between two points represents the bridge connecting them, which simplifies rivers, islands and bridges into a network and turns the problem of seven bridges into a problem of judging whether the connected networks can draw a sum. He not only solved this problem, but also gave the necessary and sufficient conditions for connected networks to be brushes, if they are connected and the odd vertices (the number of arcs passing through this point is odd) are 0 or 2.
When Euler visited Konigsberg, Prussia (now Kaliningrad, Russia) in 1736, he found that local citizens were engaged in a very interesting pastime. In konigsberg, a river called Pregel runs through it. This interesting pastime is to walk across all seven bridges on Saturday. Each bridge can only cross once, and the starting point and the ending point must be in the same place.
Euler regarded every land as a point, and the bridge connecting the two lands was represented by a line.
It was later inferred that such a move was impossible. His argument is this: In addition to the starting point, every time a person enters a piece of land (or point) from one bridge, he or she also leaves the point from another bridge. So every time you pass a point, two bridges (or lines) are counted, and the line leaving from the starting point and the line finally returning to the starting point are also counted, so the number of bridges connecting each piece of land and other places must be even.
The graph formed by the seven bridges does not contain even numbers, so the above tasks cannot be completed.
Euler's consideration is very important and ingenious, which embodies the uniqueness of mathematicians in dealing with practical problems-abstracting a practical problem into a suitable "mathematical model". This research method is called "mathematical model method". You don't need to use profound theories, thinking is the key to solving problems.
Next, based on a theorem in the network, Euler quickly judged that it was impossible not to visit the seven bridges in Konigsberg at one time. In other words, for many years, the non-repetitive route that people have worked so hard to find simply does not exist. A question that stumped so many people turned out to be such an unexpected answer!
1736, Euler expounded his method of solving problems in the paper report of "Seven Bridges in Konigsberg" submitted to Petersburg Academy of Sciences. His ingenious solution laid the foundation for the establishment of a new branch of mathematics-topology.
3. Consider one side first: 60/5= 12, that is, there is a segment of 12 in the middle, so the total number of people is the end points of the line segment, that is, 12+ 13. You can draw two continuous line segments and check that their endpoints are 2+ 1.
So the total number of people is 13×2=26.
4. It is known that 10/2 has been sawed into five segments, but when there are 4 meters left in the end, sawing once is enough, so only four words are needed to be sawed, so the time required is 4×4= 16 minutes.
The largest 7-digit number is 8765432 and the smallest 7-digit number is 1023456, so the difference between them is 774 1976.
6. At least one number in any five consecutive singular numbers must be a multiple of 5 and 2. The unit number of 5 multiplied by 2 is 0, and 0 multiplied by any number is 0, so the unit number is 0.
7. The number of girls is 60×(3/5)=36, and that of boys is 60-36=24, 36-24= 12, so boys need to add 12.
8. Its length is 1×20=20, so its circumference is (20+ 1)×2=42.
Will it! Are you satisfied?