Can you draw the fifth ring of the Olympic Games in one stroke? The question is not difficult, just draw with a pen and you will know the answer.

Li Xuan just remembered the story of Eula Seven Bridges that he saw in elementary school mathematics textbooks before.

In the eighteenth century, in a park in Cornisburg, seven bridges connected the two islands and banks of the river. One day, someone asked a question: Can you walk across all the bridges once?

The way to walk the seven bridges is calculated to be 7x6x5x4x3x2x1=5040. The stupidest way is to verify them one by one. At that time, no one found the answer to the seven bridge problem, and a group of college students were also confused and wrote to Euler to find an answer.

If you walk through n bridges at one time, or if you can cut a square with scissors at one time, this type of question is actually equivalent to whether you can draw a certain shape in one stroke.

Based on the seven bridge problem, Euler abstracted the mathematical problem of drawing a certain graphic problem with one stroke, and proposed the conditions for drawing one stroke: one is that the graphics must be connected, and the other is that a stroke must have a starting point and an end point.

The starting point has an outgoing line, no back line, and the end point is the opposite. There are incoming lines and no outgoing lines. No matter how you wind it, you need to draw one stroke. The starting point and the end point can always extend an odd line segment. This point is called an odd point. In other words, if there are 0 or 2 intersections of a geometric figure line segment, you can draw one stroke.

For example, a square has 0 odd points, which can be drawn in one stroke.

Of course, if you find the right idea, the problem will be very simple. Elementary school students can understand it, and it will be done with just one sentence.

He can be called a mathematician, and he has great abstract thinking, and has strong ability to convert problems in equivalent conversion. He knows how to simplify complex problems. Ordinary people can understand the method of proof, but don’t know how to think of the idea, and they will only think of the problem in complexity. This is not possible for abstract thinking.

This story is very famous in the history of mathematics.

Li Xuan always has a lot of insights when he thinks about it. For example, the math level of college students in the 18th century was worrying, and even such a simple problem was confused.

All are parallel goods.

Perhaps it is not as good as the junior high school students today. They are studying plane geometry in junior high schools. Many college students couldn't understand it hundreds of years ago.

Of course, no matter how much you complain, Li Xuan also knew that this was the limit of the times. Science was at the beginning of that time, because the process was slow, and every step was difficult and great. Without the crawling of the past, there would be no running today.

In his heart, Li Xuan was just a pity that there was no Chinese involved in the crawling stage of science, so that all the basic theories of science in junior high schools and high schools are named by foreigners.

The theories in textbooks are not difficult, but ancient China lacked the atmosphere of scientific thought and could not develop theories.

This has to mention the Bible "Geometric Origin" in the history of mathematics. If there were Euclid's scientific thoughts in "Geometric Origin" in ancient China, it would not rely solely on empiricism. Based on the ancient population base of China, the speed of scientific development would be unimaginable.

Unfortunately, "The Original Geometry" was officially introduced to China. It was already the late Ming Dynasty. Xu Guangqi first translated points, lines, angles, and geometry. Later, this translation also traveled to Japan...

Various reasons in the past have led to the difficulty of scientific development in ancient China.

Li Xuan can only sigh now that the cradle of ancient Greek civilization, the science of ancient Greek civilization, is at least one successor, and it would be great if it was not broken.

The Euler Seven Bridges issue laid the foundation for the later establishment of graph theory, which Euler is also called the founder of graph theory.

Graph Theory is one of the research objects of combinatorial mathematics (also known as discrete mathematics). One of the four major contents of high school mathematics competitions is combinatorial mathematics, which has always been a difficult point. Of course, the examination content rarely involves graph theory.

"Do you know how to do this question?" Li Xuan looked at the question of drawing the fifth ring of the Olympic Games and asked Xu Xindi with a smile.

But beyond Li Xuan's surprise, Xu Xindi nodded proudly, "Of course I understand, I can draw it in one stroke."

Li Xuan was speechless and suddenly realized that this little guy was very powerful. He was in the sixth grade of elementary school, and he read the story of Euler Seven Bridges in the People's Education Press. He knew a stroke problem and others understood it in the third grade. He could only tell the starting point differently...

Fortunately, I have a system.

Li Xuan was filled with emotion for a moment. It was rare to be so smart and educated when he was a child. Perhaps this was the child from the "official family", unlike those naughty children outside, and asked with a smile: "Then do you know why?"

"Because I've drawn it in one stroke."

“…”

Li Xuan was speechless and thought that this little guy really understood the reason, and it was empiricism for a long time. Yes, he could indeed draw one stroke after another, but in this way he had no scientific thinking and was just relying on experience to do the questions.

The following time, Li Xuan patiently explained to Xu Xindi a method of proof of strokes.

He did not instill knowledge points, nor did he even ask Xu Xindi to remember them, but only talked about the way to think, what conditions should be required for one stroke, and why, it was not like class, but more like chat.

If scientific thinking is enlightened, once the thinking method is understood, similar questions will not be difficult for him. While listening to Li Xuan's story, Xu Xindi thoughtfully and nodded constantly.

Li Xuan often asks Xu Xindi some small questions.

"Xindi, if you ask if you can use scissors to cut the Olympic Five Rings at one time, is it the same as drawing the Olympic Five Rings in one stroke?"

“Same.”

“Awesome.”

"whee."

Xu Xindi was disgusted with Xu Lingchu finding a tutor for him at first, but he had to agree due to his sister's threat. He remembered that under the coercion of his sister, he was very resistant in his heart when he asked his mother to find a tutor for him, but now he likes Li Xuan more and more. "Sister Li Xuan, you are so clear about it, I will understand it immediately."

"Uh..." Li Xuan shook his head helplessly and decided to tell the little guy the truth, "I am my brother."

"Brother?" Xu Xindi frowned and nodded immediately, understanding, "Okay, if you want to be a brother, I will call you brother."

Li Xuan was so amused that he suddenly thought of something and said with a smile: "Would you like me to be your brother-in-law?"

Xu Xindi was stunned for a moment, looked up at Xu Lingchu, "Does sister like you?"

"What if you like?"

"...Sister likes you, and I like you too, that's OK."

"I agreed that we will be a family in the future."

Xu Lingchu kept watching quietly. Li Xuan liked her younger brother, so she was very happy and satisfied with her younger brother's performance.

Because of the question Li Xuan suddenly raised, her face suddenly turned a little red, and there was light in her eyes, but in a blink of an eye, she was warmed by the conversation between Li Xuan and her brother.

Xu Lingchu smiled secretly, and the corners of his mouth outlined a beautiful curve.

Li Xuan is so gentle and pleases his younger brother, with such a good attitude, and is patient and meticulous. He has clearly said that he doesn't like the little boy the most, but she is worried that Li Xuan will dislike his younger brother being stupid.

This change in painting style made her feel a little unexpected. She was very beautiful. The scenes and sounds of Li Xuan and his younger brother chatting are still clearly presented in her memory many years later.

Finally, Li Xuan asked a question, "Xindi, do you know that we are on the earth, standing on a round earth, why don't we leave the earth and fall into the universe? Think about it carefully, and I will reward you with good things after I come up with it."

Li Xuan planned to use this question to let the little guy know that life experience may be wrong.

Xu Xindi indeed frowned and fell into thinking.

...

...

The primary school mathematics Olympiad is related to the transition from elementary school to junior high school. After Li Xuan taught Xu Xindi, he was still a little moved.

The times are progressing, technology is developing very rapidly, and students' level is also improving. Students' literacy is improving from elementary school to university. There may not be any difference in a few years, but compared with the last century, it is obvious that the improvement has been felt.

Once you don’t study, you will feel a sense of crisis that you are eliminated by the times. It is becoming increasingly difficult to be a top student. The new wave of the Yangtze River pushes the old wave.

Hundreds of years ago, when the "Prince of Mathematics" Gauss got 1+2+3+4...+100 simple calculation method. In his time, only geniuses could think of it.

But today, whether it is the Fibonacci sequence or any other variety of sequences, as long as it is a series-related problem, for top mathematics students who can enter the training team, it is all a bonus question.

This leads to the fact that the basic sequences are not taken directly in the exams of CMO. Only the first test of the provincial league will involve sequences, and the second test will not be taken directly, for fear of giving too many points to expand the gap.
Chapter completed!