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.

Euler used points to represent islands and land, and the connecting line between the two points represented the bridge connecting them, which simplified rivers, islands and bridges into a network, and turned the problem of seven bridges into a problem of judging whether the connected networks could draw a sum.

Extended data:

1736, 29-year-old Euler submitted his paper "Seven Bridges in Konigsberg" to St. Petersburg Academy of Sciences. While answering questions, he created a new branch of mathematics-graph theory and geometric topology, which also opened a new course in the history of mathematics.

After the "Seven Bridges" problem was put forward, many people were interested and tried it one after another, but for a long time, it was never solved. Through the study of seven bridges, Euler not only satisfactorily answered the questions raised by Konigsberg residents, but also drew and proved three more extensive conclusions about a stroke, which people usually call "euler theorem F".

inference method

When Euler visited Konigsberg (now Kaliningrad, Russia) in Prussia on 1736, he found that the local citizens were engaged in a very interesting pastime. In konigsberg, a river named 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 each 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.

Baidu Encyclopedia-Seven Bridges Problem