If the number of lines from a point is odd, we call this point a "singularity". What needs to be understood here is that "starting" does not mean "passing", and "starting" means starting from this point every time. As shown in figure 1, there are five lines from the red dot, and 5 is odd, so the red dot is singular; The number of lines includes the number of straight lines and curves. As shown in Figure 2, there are three lines from the red dot, and 3 is an odd number, so the red dot is a singular point.
The origin of stroke
/kloc-In the 8th century, in a park in Konigsberg, there were seven bridges connecting two islands in the Fritz fritz pregl River and their banks. Can we start from any of these four places, cross each bridge only once, and then go back to the starting point? After the problem of the Seven Bridges was put forward, many people were interested in it and tried it one after another, but for a long time, it was never solved, thus forming the famous "Seven Bridges in Konigsberg".
1735, several college students wrote to Euler, a talented mathematician who worked at the Academy of Sciences in Petersburg, Russia, and asked him to help solve this problem. After personally observing the seventh bridge in Konigsberg, Euler seriously thought about the way to go, but he never succeeded.
After a year's research, 1736, 29-year-old Euler submitted his paper "Seven Bridges in Konigsberg" to St. Petersburg Academy of Sciences. While answering questions, he founded a new branch of mathematics-graph theory and geometric topology, and thus launched a new course in the history of mathematics.