I Kidnapped An Alien Civilization

2021-07-07

Chapter 32 The Eagle and the Hedgehog

Li Mo found that no matter how early he went, the library was always full of people. He quietly came to a small corner, fearing that something like the last time would happen again.

I took out the manuscript paper, but couldn’t write. Perhaps it is because the definition of the four-color conjecture is very simple. Simple means that there are few starting points, and it is difficult to use a mature theorem system to interpret it.

The four-color conjecture is like a hedgehog.

Hedgehog! Li Mo remembered the story told by the old man in the basement of the library, “How did I answer it at that time?”

“If I were this eagle, I would catch this hedgehog high in the sky, Fall.” Li Mo clearly remembered his answer.

“The four-color conjecture is equal to a hedgehog, and what does it mean to catch a high altitude?” He felt that he was about to grasp the crux of the problem, and he was just a little short.

“The four-color conjecture equals a hedgehog, the four-color conjecture equals a hedgehog, and the four-color conjecture equals a hedgehog.” Li Mo kept reciting in the heart, suddenly a dive light flashed in his mind.

“The four-color conjecture is equal to a hedgehog, so I can put this hedgehog in the three-dimensional coordinate system, and then I can use it to perform precise strikes.”

Li Mo felt that he had already Touching the threshold, he took out a piece of paper and wrote on it: We can convert the four-color conjecture, or the four-color theorem, from a “map” to a “three-dimensional coordinate system” equivalently. A graph, loosely speaking, is a graph formed by connecting points and edges. In graph theory, there is a definition called a plane graph, which means that a graph can be drawn on a three-dimensional coordinate system, and the edges do not intersect each other. We regard each country on the map as a point, and two countries adjacent to each other mean that there is an edge between these two points. In this way, we get a three-dimensional coordinate system, and coloring the country becomes the coloring of the points in the coordinate system, so that adjacent points are different colors. The four-color theorem says that for any three-dimensional coordinate system, four colors are enough to satisfy the above conditions.

What we need to do now is to find out that mysterious function. A graph with more than or equal to five points connected in pairs cannot be drawn in the coordinate system. First consider coloring the vertices of a given graph G so that the two vertices of any edge have different colors. We call the minimum required number of colors satisfying the condition chromatic.

At the same time, we call the number of points of the largest complete graph subgraph contained in the graph f as the clique number, denoted by x. It is easy to find that a complete graph of n points requires at least n different colors because the points are adjacent to each other.

Let x(n) be a sequence of M items, which can represent any lattice of graph theory. By DFT transformation, the calculation of any X(m) requires M complex multiplications and N-1 complex numbers Addition, then it takes about M^2 operations to find the X(m) of the NM-term complex number sequence, that is, the N-point DFT transformation. When N1=10 points or more, N3=10486 operations are required.

From the above, it is obvious that a graph is arbitrarily divided and each part is colored, so that any graph with a common edge Sections have different colors, and only four colors can be used, no more. This proposition is established.

Certificate completed.

Li Mo, who broke through the barriers of thinking, wrote down all the ideas of proof in one breath. No wonder so many mathematicians have fallen before the four-color conjecture over the past century. It looks very weak like a hedgehog, but it is actually difficult to find a place for its mouth. If a weakness is found, it is nothing more than a difficult proof problem.

Looking at the complete proof idea on the paper, Li Mo was filled with joy, he felt that he was working hard for a small step forward for human civilization. Humans are curious creatures, and exploring the unknown is an innate instinct of human beings, and it is precisely because of this instinct that human beings can stand out from many biological clocks and establish the current Earth civilization.

The next step he has to do is to sort out the papers, which is the easiest thing for Li Mo, who has the ability to write academic papers.

“Buzz. Buzz” The phone vibrated, Li Mo picked it up, and Ying Sa Sa said on WeChat: “Li Mo, why didn’t you come to the linear algebra class, if the teacher wants all the staff Big name, come quickly.”

“Oops”, Li Mo looked at the time on his phone, secretly said in one’s heart is not good. It’s just that he was so fascinated by the problem-solving that he forgot that there was another linear algebra class in the morning.

He didn’t have time to tidy up, put the straw paper in his schoolbag, and went straight to the lecture room.

There were very few students on the road. Li Mo ran and checked the time on his mobile phone, “No, I can’t catch up.”

Sure enough, he came to the amphitheater and the fruit on the podium. The teacher has already started the roll call.

“Zhang Yu!”,”Arrived!”

“Wang Chunyan!”,”Arrived!”

“Su Yuhang!”,”Arrived!”

Li Mo tiptoed to the back door, looked over his head, and found that the fruit teacher was concentrating on calling the flower list. He was about to quietly and slowly slip to his seat.

The fruit teacher on the podium: “Li Mo!”

Li Mo, who was sneaking in through the back door, replied subconsciously: “To!”.

” Terrible!”

Aware that something was wrong, Li Mo raised his head and looked at the podium. On the podium, the teacher stared at him with round eyes, waved at him and said, “This classmate, are you just here? Come, please come to the podium first.”

Li Mo had no choice but to Slowly walked to the podium under the watchful eyes of the students.

“I dare to be late for my class, it seems that my prestige has dropped a lot.” Guo teacher said with a smile, “Li Mo in the advanced math class, right? It’s not difficult for you, If you can solve a question I have, don’t blame me. If you can’t answer it, you won’t want the final grade.”

He wrote angrily on the blackboard: Vector α=(a1, a2, a3)β=(b1, b2, b3) a1!=0 b1!=0 α^Tβ=0 A=αβ^T

(1) Find A^ 2

(2) Eigenvalues and eigenvectors of matrix A

After writing, he handed over the chalk in his hand and said with a smile: “Please, Li Mo. ”Li Mo took the chalk and pondered for a moment, nodded to the fruit teacherT2

Because a^Tb=a1b1+a2b2+a3b3 = b^Ta =0

so duA^2=a 0 b^T

so A^2 is a 0 vector

2) A

a1b1 a1b2 a1b3

a2b1 a2b2 a2b3

a3b1 a3b2 a3b3

|A-λE|= 0

To directly find the determinant, the constant term and the λ first-order term are all eliminated;

Use a1b1+a2b2+a3b3=0 to also eliminate the λ quadratic term;

The last λ^3=0, the eigenvalues are all 0

Ax = 0

Because each row of A is proportional, the rank is 1

The last Eigenvector expression: x1=-b2/b1x2-b3/b1x3 (b1!=0)

In one go, Li Mo handed back the chalk and was staring at the blackboard in a daze, his face gradually changing The green fruit teacher went straight back to his seat.

After a long time, the fruit teacher on the podium reacted, and embarrassedly laughed and said: “This student named Li Mo answered very well, this time the roll call is over, let’s start. Class.”

(End of this chapter)