"What......" For a moment, Ao Liu's mouth felt dry. Pen & Fun & Pavilion www.biquge.info

"Oh, this should be what I know, about hyperbolic geometry - after all, I don't study this field very deeply, and the content above is about 700 years ago that our human race researched, because it is more common in some practices, so I will write it down. Well, newer stuff, I don't know much about it either. Wang Qi barely squeezed out a "kind look" and said, "Take a closer look, I don't think the questions you want to ask me will exceed this range." If you don't think this will solve your problem, then you can come to me again and ask for a detailed ......."

If it weren't for the fact that he could control every pore of himself, Ao Liu would have been dripping with cold sweat.

In fact, all he could read was the first seven lines of the first column. This includes a "fifth postulate", a strange saddle-like concave, a curved figure, and several vertical figures.

He can still understand the most intuitive things written in the Terran language. And the further he went, the deeper the knowledge points became, and he couldn't even guess the role of the operator.

Perhaps anticipating this dilemma, Wang Qi deliberately wrote a note next to it to explain the usefulness of each knowledge point, and ordered the words "teacher's words" to be marked.

"This ...... This ...... "Oro was very shocking. The question he came up with by himself was only in the fifth row of the first column of Wang Qi's annotated knowledge points. At that time, he spent all his time trying to learn how to prove that "the sum of the inner angles of a triangle in the geometry of the ocean is always less than half of the day of the week." However, this is only a very high part of Wang Qi's list of arithmetic knowledge. He wanted to ask another question that had not yet been solved by updating the demon clan, but that question ......

I didn't qualify for the second column.

Wang Qi simply sat on the lectern, scratching his head without any image. In the eyes of many demon clans, this image is like a monkey catching lice. He yawned, "Hey, do you have any ideas, what questions do you want to ask? If not, sit me down. ”

Aoliu's face flushed slightly. He glanced at the moonfall glaze that was smiling and twitching, and the white strings with a grotesque face, gritted his teeth and said, "You are also a species valued by the Holy Clan, and it is not unusual to learn this skill from the Holy Clan." ”

"'Skill'?" Wang Qi raised his eyebrows. For the disciples of the Ten Thousand Methods, this can be called offensive: "Skill...... It seems that the dragons didn't expect much from you in the past......"

"Insect Carving Trick ......"

Hearing the words of Aoliu Shen Lanjiao, Bai Xian Suzheng wanted to say something, but was pulled by the moonfall glass. Bai Xian Su Zheng was a little strange: "Your Highness...... If you don't say it, ......"

She actually wanted to say that in this field, the human race has relied on the acquired wisdom to come to the place where the dragon race relies on the innate surface space cognition and experience accumulation. Most of the calculations listed by Wang Qi are very intuitive to her and she can understand them at a glance. However, the latter also made her feel a little difficult - about the same as the last big question in mathematics in the college entrance examination or something?

The Terrans are not much different from the Dragons in this regard, and even vaguely more than a few points.

The moonset glass passed into the secret: "It's very interesting to watch the play." ”

Ao Liu also noticed Moonfall Liuli's actions, and he said with annoyance: "This Highness of the Holy Clan is familiar with you, and it is normal for you to understand these things. Let's talk about something else. ”

Wang Qi nodded: "Okay"

"In contrast to the geometry of the Holy Clan's oceans, there is another kind of geometry. Although the Holy Family knows it, it has never taught us, and I don't think it will ......."

Wang Qi grabbed the long sword beside him and swung it forward. Everyone saw only a sword light. Later, the walls made of ice were smoothed and carved with new words, and ice chips fell in a torrent. Wang Qi blew lightly, and it was like a light snow in the room: "Okay, okay, let's see, is this what you are asking? Is the content on it?"

The so-called "ocean geometry of the Holy Family" is nothing more than hyperbolic geometry – known on Earth as Lobachevsky geometry. In the ocean, "sound" is a better medium for transmitting information than "light". Many marine creatures rely on "singing" for positioning. The speed at which sound travels through water is closely related to the density of the water. The deeper the position, the faster the speed of sound. Therefore, in the perception of some marine creatures, the world "looks" as a sunken sphere centered on the surface of the sea. And this perception extends infinitely, and it becomes hyperbolic geometry.

In the words of the earth. According to the voices they heard, they lived on a Poincaré disc.

The oldest dragons rely on sonar to perceive the world. Their innate sense of space is Roche geometry. And when they have civilization and cultivation means, they learn to use their eyes, and naturally they can easily discover European-style geometry. After knowing Euclidean geometry, it is not too difficult to discover Rie's geometry.

This is how many marine species develop geometry. They lagged behind in the "use of fire", but they were compensated for this.

For a race that is born only by eyes, this process is many times more difficult.

Ao Liu just asked about hyperbolic geometry - Roche geometry, so now it must be Rie geometry.

The successor of Shen Lanjiao had a trance-like look in his eyes, feeling that his worldview had been challenged. He said: "In this geometry, there are infinite secrets of time and space......

Wang Qi didn't bother to laugh at her face. He backhanded and added something to the end of all the knowledge points, which is the application of Riemannian geometry in the theory of relativity, including Minkovsky space. For Li geometry, Wang Qi's cognition is more profound, because this is more used in physics.

"I said, students of the Shenlan Jiaojia family, do you want me to write a specific method again?"

Aoliu's face changed: "I can brush pictures and draw, and the role of writing symbols is limited...... Didn't you say that arithmetic is the study of computing? Let's compare calculations again!"

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

Oroyu rejoiced in his heart. Fortunately, one of his acquired teachers is also a master of arithmetic, and he has a secret solution, and he once broke the Tianyuan formula listed by thirty-three demon clan arithmeticists......

This solution is all secretly passed down by his acquired teacher, and few people know it.

Just as he was distracted, Wang Qi had already used his sword qi to burn the conclusion under his feet. Oroyu hasn't even come to his senses yet. He exclaimed, "So fast! This can't be ......."

Wang Qi just glanced at it and solved his equation, which was even shorter than the time he set the value first and then deduced the equation!

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

Aoliu's face flushed. He pondered for half an hour, and Wang Qi was not in a hurry, so he waited so full. After that, he wrote down another equation - the quadratic equation.

Wang Qi still glanced at it and answered casually.

"If you come up with a five-fold Tianyuan [fifth-order equation], I will still look up to you. Wang Qi said: "If there is anything else, just come out and take a look." ”

At first, he really hoped that the other party would ask something he didn't know. Because that means that there may still be a part of the field that the human race does not understand in the field of non-Euclidean geometry - this part may be a blind spot formed by the difference in the "innate sense of space".

However, now it seems...... Huh.

As if grasping at a life-saving straw, Ao Liu said, "There is no precise solution to the Five Heavenly Yuan in your mouth. ”

"Hehe" Wang Qi rolled his eyes and said, "Everyone, I hope that when you learn from me, you can get rid of the old ideas in your minds." According to my original plan, I will probably teach you how to solve the Fivefold Heavenly Yuan next year...... What about the original plan. ”

For a moment, Ao Liu wanted Wang Qi to really solve a fifth-order equation to see. However, he did not say it.

He still had at least a little sanity, knowing that Wang Qi would not joke about this matter. And after saying it, the most likely thing he is to bring shame on himself - he probably doesn't understand the solution at all.

Wang Qi stared at Aoliu, and finally had some regrets.

The equation of the fourth to the fifth degree is actually a huge threshold. Primary equations, quadratic equations, and even most cubic equations can be solved in a very intuitive and very simple way. The biggest breakthrough in this is probably the introduction of the concept of "imaginary numbers".

The square root of a negative number, which is unimaginable in the eyes of most ancient arithmeticists.

And after the quadratic equation, the difficulty of the equation begins to surge. Quadratic equations can be solved in a simple way, but fifth-order equations are completely incompatible.

Even if you make up a fifth-order equation with pre-prepared numbers, those numbers can only be used as one of several solutions to the fifth-order equation.

Many solutions of fifth-order equations are expressed nested with each other, and this expression often contains many kinds of "symmetric operations".

Yes, symmetry. At this point, "group theory" is needed to solve the equation. He was basically sure that it would be incomprehensible to update the arithmetic level of the demon clan.

After all, renewing the civilization of the demon race is not based on mathematics. They have their own system of speculation.

Wang Qi jumped off the desk and said, "You have asked me so many questions, I will ask you a question now, it's not too much, right?"

Ao Liu was stunned for a moment, gritted his teeth and said, "If you use unsolvable problems to pressure me......"

"Rest assured, there is no need to deal with you without solving the problem. I can assure you that it's very simple. Among the human race, the study of arithmetic is basically known. ”

Although Oroyu 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.) )