Zhan Guyue said: "Let's walk around first."
They came out of their residence and walked for a while and saw a lake. The lake is turquoise, like a mirror, and you can see the shadows of the trees. The human figure is also reflected on it.
There are several dams in the middle of the lake. Looking from each edge point to the middle, they converge to the same point in the middle. It's like an umbrella, with the circle cut into several parts from the middle. The middle circle is full of deep lake water, surrounded by a circle of dams, and the outer circle is filled with fine sand and stones. There may have been water, but it has dried up.
Several people are here measuring the area between the dams. He murmured and used paper to calculate. Zhan Gu asked them what they were doing. Those few people said it was nothing, just measuring the area.
There was a man who was tall and tall, like a calf, very strong; he had curly hair that was worn on his head like a hat; he had a long face.
There was a man next to him, short, fat, with strong shoulders, a square mouth and a black beard.
"Are you raising fish here?" Dong Chu asked.
"Yeah, otherwise what can I do here?"
"What are you measuring?" Dong Chu asked casually.
"Let's see how this fish pond can be renovated."
Liu Mozhi said: "The fish ponds here are all very good. It seems that you have been studying here."
Several people looked at the fish pond and wondered what the purpose of building so many dams in the middle was. Maybe each household would raise fish separately. Why are there deep water areas and shallow water areas? They are not experts in fish farming and cannot understand what is going on.
Look at the water, crucian carp and grass carp are swimming around.
Liu Mozhi said: "I originally thought it was a farmhouse for fishing."
Zhan Guyue said: "It's possible. Look, there are small rooms next to it, maybe restaurants and shops. Each shop has a small fish pond, separated by a dam, so they don't interfere with each other. Each customer takes a fishing rod and fishes by himself. Find a chef to do it then.”
Dong Chu said: "But I didn't see any fishing tools."
Liu Mozhi said: "I am in the fish growing season. Don't disturb others."
Dong Chu said: "Okay, let's take a look at the surrounding scenery. Take a look at the lake. But the lake is divided into these pieces, and I always feel that it doesn't look good. It turns out that it is a whole, like a mirror."
Liu Mozhi said: "There are lakes in other places, go and have a look elsewhere."
A few people continued walking, and others encountered several lakes. There were no dams to separate them, and there were no houses next to them. They were all natural scenery.
When we got to the lake, there was a restaurant written on the house, so we went in to eat.
In the morning, it was wet and cold. In a dark corner, several people were singing quietly and drinking wine. There was an elder and a young man. The elder's name is Tang Ling, who is particularly vicissitudes of life. He has a thread hat in his hand and a reserved expression on his face. The young man's name is Yu Cheng. He looks childish and very fashionable. There is a simple fishing rod next to him. A shy look on his face. There are peanut cakes and dried tofu on the table. They were having a conversation with their boss about chrysanthemum tea. He bargained and said: "Why is it so expensive?" The boss said: "This is a famous product in the town. The weather affected some time ago and the output was reduced. The price is currently like this, clearly marked." Tang Ling ordered tea and drank it. , while talking about recent research in the mathematical community. Yu Cheng listened carefully, with a look of admiration on his face. There seems to be a tacit understanding between the two.
Zhan Guyue stepped forward and said, "This senior looks familiar. Is he Mr. Tang?"
Tang Ling said: "Yes."
"We came here at the invitation of Mr. Jiang, but there is still no news from him."
Tang Ling said: "We were also invited by him. It's strange that we haven't contacted him yet. Although he is usually very busy, he doesn't even care about the people he invited. If he doesn't reply in two days, we will go back."
Zhan Guyue said: "Have you seen that strange lake separated by a dam in front? Do you think it has any special function?"
"When I saw this lake, I thought of something. It was very familiar. It seemed to be some kind of shape, but a moment passed and I couldn't remember it anymore."
Tang Ling thought for a while and said: "The first thing that came to mind was the four-color conjecture. In mathematical language, it means: arbitrarily subdivide the plane into non-overlapping areas, and each area can always use the four numbers 1234. To mark one without causing two adjacent areas to get the same number. The adjacent areas referred to here refer to a whole section of the boundary that is common. If the two areas only meet at one point or a finite number of points, it will not They are called adjacent. Because coloring them with the same color will not cause confusion. The essence is the inherent property of the two-dimensional plane, that is, two straight lines that intersect without a common point cannot appear in the plane. Many people have proved that the two-dimensional plane It is impossible to construct five or more two-by-two connected areas, but it does not rise to the level of logical relationships. It promotes the development of graph theory. Using computers to do proofs and making tens of billions of judgments is ultimately just a problem in a huge Success is based on numerical superiority, but this does not conform to the logical system of mathematics."
"Kempe's proof illustrates two important concepts. The first concept is 'configuration'. He proved that in every regular map at least one country has two, three, four or five neighbors. For countries, there is no formal map where each country has six or more neighbours, that is, a set of configurations consisting of two neighbours, three neighbours, four or five neighbours, is Inevitably, every map contains at least one of these four configurations. Another concept proposed by Kemp is 'reducibility'. He proved that as long as a country in a five-color map has four neighboring countries, there will be A five-color map with a reduced number of countries. Since the introduction of the concepts of configuration and reducibility, some standard methods for checking configurations to determine whether they are reducible have been gradually developed, which is an important basis for proving the four-color problem. But to prove large configurations Reducibility is quite complex.”
"Haken and Appel collaborated to compile a very good program. In June 1976, they spent 1,200 hours on two different computers and made 10 billion judgments, finally completing the proof of the four-color theorem. .”
Zhan Guyue said: "The pattern of this lake is somewhat similar to the four-color problem. The lake surface is cut into many pieces. But the number of pieces is too small, and there are still doubts."
Liu Mozhi said: "Maybe it's some kind of geometric problem."
Dong Chu said: "I don't know if it is another topological problem."
Topology is a branch of geometry, but this geometry is different from ordinary plane geometry and solid geometry. The usual research objects of plane geometry or solid geometry are the positional relationships between points, lines, and surfaces and their metric properties. Topology has nothing to do with the length, size, area, volume and other metric properties and quantitative relationships of the research object.
Yu Cheng said: "Let's leave our contact information. If Mr. Jiang contacts us, we will notify each other."
Zhan Guyue said: "Okay."
They found a seat and ordered breakfast with the boss, including fried dough sticks, wontons with bamboo shoots and bean paste cakes.
