Enter the Immortal Cultivation

"What..." For a moment, Ao Liu felt dry in the mouth.

"Oh, this should be what I know about hyperbolic geometry - after all, I haven't studied this field very deeply. The content above is probably what our human race studied about 700 years ago. Because it is more common in some revisions, I wrote it down. Well, I don't know much about newer things." Wang Qi forced a "kind look" and said, "Take a closer look, I think the questions you want to ask me will not exceed this range. If you think the content above can't solve your problem, then come to me for details..."

If he couldn't control every pore of his body, Ao Liu would definitely have been sweating.

In fact, he could only understand the first seven rows of the first column. It includes a "fifth postulate", a strange concave surface similar to a saddle, a figure composed of curves, and several vertical graphs.

These most intuitive things written in human language, he can still understand. And the more you go back, the deeper the knowledge points here are, and he can't even guess the role of operators.

Perhaps Wang Qi had anticipated this dilemma, so he wrote notes on the side to explain the usefulness of each knowledge point, and emphasized the words "Teacher's words".

"This... this..." Ao Liu was shocked. The question he came up with was only in the first column and fifth row of the knowledge points marked by Wang Qi. Back then, he had worked hard just to learn how to prove that "the sum of the interior angles of a triangle in the ocean geometry is always less than half of the Zhoutian". However, this was just a very advanced part of the mathematical knowledge listed by Wang Qi. He wanted to ask another question that the newer demons had not yet solved, but that question...

was not qualified to enter the second column.

Wang Qi simply sat on the desk and scratched his head without any image. This image looked like a monkey catching lice to many demons. He yawned: "Hey, hey, do you have any ideas? What questions do you want to ask? Class is in session now. If not, sit down."

Ao Liu's face flushed slightly. He glanced at Yueluo Liuli, who was laughing so hard, and Baixian Suzheng, who had a weird look on his face, and gritted his teeth and said, "You are also a species that the Saint Clan values. It's not surprising that you learned this skill from the Saint Clan."

"'Skill'?" Wang Qi raised his eyebrows. For the disciples of Wanfamen, this was an offense: "Skill... It seems that the Dragon Clan didn't have very high expectations of you in the past..."

"A trifling trick..."

Hearing the words of Aoliu Shenlanjiao, Baixian Suzheng wanted to say something, but was pulled back by Yueluo Liuli. Baixian Suzheng was a little surprised: "Your Highness... If you don't say it, okay..."

She actually wanted to say that in this field, the human race has relied on acquired wisdom to reach the same place as the dragon race, which relies on innate curved space cognition and experience accumulation. Most of the formulas listed by Wang Qi were very intuitive to her and she could understand them at a glance. However, the latter ones also made her feel a little difficult - about the same as the last big question in the college entrance examination?

The human race is not much different from the dragon race in this regard, and even slightly surpasses it by a few points.

Yueluo Liuli whispered: "It's quite interesting to watch the show."

Aolu also noticed Yueluo Liuli's behavior, and he said in annoyance: "This Saint's Highness is familiar with you, it's normal for you to know these things. Let's talk about something else."

Wang Qi nodded: "Okay"

"In contrast to the Saint's ocean geometry, there is another kind of geometry. Although the Saint knows it, it has never taught us, and I don't think we know it..."

Wang Qi grabbed the long sword beside him and swung it forward. Everyone only saw a flash of sword. After that, the wall made of ice was smoothed and new words were engraved, and ice chips fell down. Wang Qi blew gently, and it seemed like snowing in the room: "Okay, okay, take a look, is this what you are asking? Is the content on it?"

The so-called "Saint's ocean geometry" is just hyperbolic geometry - it is called Lobachevsky geometry on Earth. In the ocean, "sound" is a better medium for information transmission than "light". Many marine creatures rely on "singing" to locate. The speed of sound in water is closely related to the density of water. The deeper the position, the faster the speed of sound. Therefore, in the perception of some marine creatures, the world "looks" like a concave sphere with the center on the sea surface. And this perception is infinitely extended to become hyperbolic geometry.

In the words of the earth. According to the sound they hear, they live on a Poincare disk.

The oldest dragon race perceives the world through sonar. Their innate sense of space is Lobachevsky geometry. And when they have civilization and cultivate means, they learn to use their eyes, and naturally they can easily discover Euclidean geometry. After knowing Euclidean geometry, it is not too difficult to discover Riemann geometry.

Many marine species develop geometry in this way. They lag behind in "using fire", but they have been compensated in this regard.

For races that rely only on their eyes, this process is many times more difficult.

Ao Liu just asked about hyperbolic geometry - Lobachevsky geometry, so what he is asking now must be Riemann geometry.

The heir of Shen Lanjiao looked dazed and felt that his worldview was challenged. He said: "In this geometry, there are also infinite secrets of time and space..."

Wang Qi was too lazy to laugh at her face. He added something behind all the knowledge points, which included the application of Riemannian geometry in relativity, including Minkowski space. Wang Qi's understanding of Riemannian geometry is even deeper, because it has more applications in physics.

"I say, students of Shenlan Jiao's family, do you want me to write another specific method?"

Ao Liu's face changed: "Those who can draw pictures and write talismans have limited use... Didn't you say that mathematics is the study of calculation? Let's compare calculations again!"

He raised his hand and wrote a formula, and then said: "Solve this!"

Ao Liu was relieved. Fortunately, one of his post-natal teachers was also a master of mathematics, and had a secret solution. He had broken the Tianyuan style listed by thirty-three demon clan mathematicians...

This solution was all secret from his post-natal teacher, and few people knew it.

Just when he was distracted, Wang Qi had already engraved the conclusion under his feet with sword energy. Ao Liu hadn't even come back to his senses. He was shocked: "So fast! This is impossible..."

Wang Qi only took a glance and solved his equation, even in a shorter time than he had to determine the value and then deduce the equation!

"You are so surprised, it's just a triple Tianyuan [cubic equation]." Wang Qi said: "If you have the ability, you can come up with a higher level?"

Ao Liu's face flushed. He pondered for half an hour, and Wang Qi was not in a hurry, just waiting. After that, he wrote down another equation - a quartic equation.

Wang Qi still glanced at it and solved it casually.

"If you come up with a fifth Tianyuan [quintic equation], I will look at you more." Wang Qi said: "If you have any other tricks, just show them."

At the beginning, he really hoped that the other party could ask something he didn't know. Because that means that the human race may still have some parts of the field of non-Euclidean geometry that they have not recognized - this part may be a blind spot in thinking formed by the difference in "innate sense of space".

But now it seems... hehe.

Ao Liu grabbed a life-saving straw and said, "There is no exact solution to the fifth level of Tian Yuan you mentioned."

"Hehe" Wang Qi rolled his eyes and said, "Everyone, I hope you can get rid of the old ideas in your mind when you study with me. According to my original plan, I will teach you how to solve the fifth level of Tian Yuan next year... the original plan."

For a moment, Ao Liu wanted Wang Qi to really solve a quintic equation. However, he didn't say it out loud.

He at least had a little bit of reason left, knowing that Wang Qi would not joke about this matter. And after saying it, the biggest possibility for him to humiliate himself is that he may not understand the solution at all.

Wang Qi stared at Ao Liu, and finally felt a little regretful.

The fourth-order equation to the fifth-order equation is actually a huge threshold. The first-order equation, the second-order equation, and even most of the third-order equations can be solved in a very intuitive and simple way. The biggest breakthrough here is probably the introduction of the concept of "imaginary number".

The square root of a negative number is simply unimaginable in the eyes of most ancient mathematicians.

After the fourth-order equation, the difficulty of the equations began to increase sharply. The fourth-order equation can still be solved by simple methods, but the fifth-order equation is completely impossible.

Even if you use the numbers prepared in advance to make up the fifth-order equation, those numbers can only be one of the solutions of the fifth-order equation.

The many solutions of the fifth-order equation are nested in each other, and this expression often contains many kinds of "symmetry operations".

Yes, symmetry. At this point, "group theory" is needed to solve the equation. He is basically sure that the mathematical level of the updated demon clan cannot understand it.

After all, the civilization of the updated demon clan is not based on mathematics. They have their own system of thinking.

Wang Qi jumped off the desk and said, "You asked me so many questions, I'm asking you a question now, isn't that too much?"

Ao Liu was stunned, gritted his teeth and said, "If you use unsolvable questions to pressure me..."

"Don't worry, I won't need unsolvable questions to deal with you. I can guarantee that it's very simple. Among the human race, those who study mathematics basically know it."

Although Ao Liu knew that Wang Qi had bad intentions, he still nodded.

Wang Qi asked, "What is length? What is area? What is volume?" (To be continued ~^~)