Due to the limited space on the whiteboard, the final steps presented are as concise as possible, so that the thinking process is ignored.
But anyone who learns Mathematical Olympiad knows that the steps of solving problems are only presented externally, and what really matters is thinking ability.
Tan Jiaxu also wanted to hear how she solved the problem, how she started, and how she thought of nesting lemmas with lemmas to prove the conclusion.
Jiang Fuyue: "Do you want to listen?"
"want-"
"good."
Tan Jiaxu returned to his seat, looked up at the podium, and for the first time showed Jiang Fuyue squarely in his eyes.
Zou Hao was amazed.
Although Jia Xu usually plays with them and everyone has a good relationship, there is always a sense of arrogance in the genius.
He didn't show it deliberately, but Zou Hao could feel it.
Now, looking at Jiang Fuyue with this kind of eyes...
It can only show that only the geniuses of geniuses can convince geniuses.
At this time, Jiang Fuyue had already picked up the pen, stood in front of the whiteboard—
"Seeing this question, many people's first reaction is to try to find the relationship between vertices and edges."
A large part of the students below nodded heavily.
That's what they think.
"We know a connected graph, assuming it has V vertices, if there are only V-1 edges, it is impossible for a circle to appear, otherwise this graph is not a connected graph."
"However, when we have V edges, there must be a cycle. Every time we add an edge on this basis, a new cycle will be created. Suppose we have V+1 edges, the graph There is only one circle in , then when we remove an edge from this circle, there is no circle in this graph, but there are still V vertices in the graph, so there must be a circle. So our assumption is not true, graph There are at least two circles in…”
Talk about praise and focus.
Zou Hao didn't want to hear it at first, but the girl's voice was refreshing and cool, like a mountain spring in a deep stream, murmuring and ding-dong.
He was attracted unconsciously.
Jiang Fuyue: "... here we need to introduce a new definition called margin, that is, the number of edges E minus (V-1), which is equal to E-V+1, which is used to describe the amount of redundant vertices in a graph , and this quantity roughly determines the number of circles in our graph."
Tan Jiaxu's eyes lit up.
That's right, this is the step!
He was thinking about how to bypass this point of proof, but Jiang Fuyue directly introduced a new definition.
He avoids risks, but she rises to the challenge.
This is the difference in the thought process of the two, which ultimately leads to the difference between success and failure.
Therefore, it was not without reason that he lost.
Jiang Fuyue stood on the podium, with a slim figure and outstanding temperament, but at this moment, almost everyone subconsciously ignored her appearance, and what they saw was her radiant wisdom, powerful logic, rigorous attitude, and her respect for others. Intellectual respect and piety.
"... If you think about it further, in fact, when there are more and more edges in the graph, there will be more and more circles, and these circles will cross each other, and the circumference of the circle will become smaller and smaller. Back to the topic itself, use The description of 'finite number of counterexamples'. If we want to solve this problem head-on, the only way seems to be to constructively find such two cycles in any graph... "
It turns out that someone's soul really shines.
It's so brilliant you can't take your eyes off it.
Ling Xuan stood beside him, tilting his head slightly, and this angle was just right so that the students below could not see the obsession in his eyes at the moment.
His heart beat one after another, and the feeling so strong that it was about to break through his chest made him both panicked and excited.
He knows that some things cannot be restrained.
For example, like it.
But he didn't even have the courage to say it.
Jiang Fuyue was too dazzling.
He used to think that he was enough to gather light, but now he realizes that Jiang Fuyue herself is the light source.
Her excellence made him retreat, and her brilliance overshadowed everyone, including herself.
Wanting, but not daring, that kind of entanglement of being unattainable has become a kind of torture.
Ling Xuan lowered his eyes fiercely, must be patient, he warned himself.
At this time, through the half-closed back door of the classroom, there is a person who is also staring at the radiant girl on the podium.
Jiang Fuyue: "... But the title tells us that there are limited counterexamples in this situation, almost telling us that this way is dead. Then we might as well change the angle: prove the lemma, use this lemma to draw the contradiction, and realize Rebuttal..."
Qingling's voice reveals absolute rationality, supported by strong logic.
The man watched and listened, with a smile slowly appearing in his eyes.
"Professor Xie?" Zhao Tiejun called softly.
Xie Dingyuan suddenly returned to his senses, but he didn't look back.
Zhao Tiejun followed the trend, and then said with a smile: "This is the Mathematics Olympiad class, isn't it about to participate in the National League, and it's training."
Xie Dingyuan hums lightly.
Director Zhao saw that he was very interested, and he couldn't help but talk about sex: "The girl who spoke on the podium is the first in the third year of senior high school. She is also the gold medalist and special prize winner of this year's IPhO and IOI. Both subjects have full marks, B and Q. Great seedlings…”
Speaking of this, Zhao Tiejun suddenly felt proud, and even his chest stood up.
"Really?" Xie Dingyuan answered calmly, giving him a chance to continue.
Sure enough, Zhao Tiejun began to chatter—
"This child is very good, and none of the subject teachers does not praise her for being smart."
Xie Dingyuan: Well, the brain is indeed more flexible, whether it is learning or being annoying.
"Get along very well with the classmates in the class. When I have free time, I will give lectures to everyone, sort out the key points and so on. Everyone calls her Miss Yue Yue."
Xie Dingyuan: Sister? Obviously still a little girl.
"Sports performance is also outstanding. I have specially practiced high jump and shot put. I often play basketball with my classmates after class."
Xie Dingyuan: Classmate? male or female
"Some time ago, I published a paper on the main page of the PRL journal. What is the title... Uh! I forgot, anyway, it is related to bacterial movement."
Needless to say, Xie Dingyuan also knows.
Maybe he was the first to see the prototype of that paper
"In short, classmate Jiang Fuyue has developed morality, intelligence, physique and beauty in an all-round way. She is a particularly outstanding student, the light of the first school!"
Xie Dingyuan nodded involuntarily, and a smile flashed in his eyes, but he heard that it had already been mentioned—
"... So, the lemma is as follows: For any positive real number a, natural number N, prove that for a proposition with N vertices, (1 + a)N edges, there is a cycle of length less than aN, and there are only finite counterexamples... "
Just listening to the sound can make him feel good.
"The only bad thing to say," Director Zhao sighed, "is that his temper is a bit stubborn and his ideas are a bit big."
"Oh?" Xie Dingyuan raised his eyebrows.
"Some time ago, the recommendation notice for B University and Q University was sent to the school, saying that she was allowed to choose a major, but I didn't expect the child to say no, so he refused. There was no room for change, and the parents also followed her around..."
Zhao Tiejun looked regretful.
That's B major and Q major!
I heard that Xu Jing, Meng Zhijian, and Yu Wenzhou ran wildly in the office that day, sighing and cursing.
And what about Jiang Fuyue
Leng was determined to go her own way, and no one could persuade her to come back.
It was the first time Xie Dingyuan heard: "Why did she refuse?"
Zhao Tiejun: "It seems that you plan to take the college entrance examination?"
Speaking of which, he was a little proud.
Do students from other schools have the courage to reject majors B and Q
No!
But there is one of them!
Not just one!
Ling Xuan also refused, good guy, can we still get together
This year is really amazing!
Xie Dingyuan withdrew his gaze, and took advantage of the opportunity to hold back the smile on his lower lip: "Let's go, Director Zhao."
"Oh, okay, student Zhong's legs are almost grown, right?"
"Um."
"That's good, that's good. In fact, you don't need to go there in person, just make a phone call, or ask Zhong to bring a letter of cancellation signed by your parents on the day he returns to school..."
Better than coming in person, right
In fact, Zhao Tiejun didn't know why this giant Buddha came down suddenly.
When the school sent him to pick him up, he was in a daze.
Xie Dingyuan stepped forward, and the voice of the girl behind him became smaller and smaller—
"Assuming that a graph has N vertices and at least (1 + a) N edges, and the lengths of all circles in the graph are different, it is necessary to construct a contradiction when N is large enough to prove that this assumption is not true. Then we You can do this to find the shortest circle in the graph..."
After returning from a teaching and research meeting in Xujing, he suddenly found that the atmosphere in the class was much more harmonious.
He asked the reason, but who knew that this group of students was stricter than the other.
"?" Curious, scratching his heart and lungs.
But he didn't struggle for too long, harmony is a good thing.
This friendly atmosphere lasted until the end of the two-week semi-enclosed training camp.
Soon, the Mathematical Olympiad National League is coming...
－－－－－Off Topic－－－－－
There is no reason, I just want to see my wife.
Zhong Ziang: Use me as a cover to save face