Due to some reasons, a large number of users suddenly cannot open the web page to visit this site today. Please keep in mind the domain name of this site EbookFREE.me (the first letter of literature + org dot com, EbookFREE.me) to find the way home!
"Wh ..." In a flash, Austrian felt dry.
"Oh, this should be what I know about hyperbolic geometry-after all, I haven't studied this field very deeply. The above content is about what our human race researched about 700 years ago, because It ’s more common in some practice methods, so I ’ll write it down. Well, I do n’t know much about the newer things.
Wang Qi barely squeezed out a
kind look
and said:
Look carefully, I miss you The question to ask me will not exceed this range. If you feel that the content above does not solve your problem, then you can come to me and ask for more ... "
If it is not possible to control every pore of his own, Austrian flow must have been cold and sweating.
In fact, what he can understand is nothing but the first seven lines of the first column. This includes a "fifth postulate", a strange concave surface similar to a saddle, a curve-shaped figure, and several vertical figures.
He can understand the most intuitive things written in human language. And the further back, the deeper the knowledge inside, he can not even speculate on the role of the operator.
Perhaps this embarrassment has been anticipated. Wang Qi specially wrote a comment next to it, explaining the use of each knowledge point, and focusing on the words "teacher's words".
"This ... this ..." Austrian was horrified. The problem he came up with was located in the fifth row of the first column of Wang Qi ’s knowledge points. At that time, he was exhausted in order to learn how to prove that "the interior of the ocean geometry, the internal angle of the triangle is always less than half the week". However, this is just a very advanced part of Wang Qi's list of mathematics knowledge. He wanted to ask another question that has not yet been resolved by the update demon clan, but that question ...
Actually did not qualify for the second column.
Wang Qi simply sat on the rostrum, scratching his head with no image. In the eyes of many demons, this image looks like a monkey catching lice. He yawned: "Hey, is that a bit of an idea? What questions do you want to ask? What about the class now. If not, sit down for me."
Austrian flow blushed slightly. He glanced at the Yueluo Liuli with a smile, and a grotesque white string Suzheng, gritted his teeth and said: "You are also a species that the holy clan values. It is not uncommon to learn this skill from the holy clan.
"'Trick'?" Wang Qi raised his eyebrows. For Wanfamen disciples, this is an offense: "Skills ... It seems that the Dragon Clan's expectations of you in the past were not very high ..."
"Carving insects ..."
Hearing Austrian Liu Shenjiao's words, Baixuan Suzheng wanted to say something, but was pulled by Yueluo Liuli. Bai Xuan Su Zheng is a little strange: "Your Highness ... Don't say anything, okay ..."
In fact, she really wanted to say that in this field, the human race has relied on acquired wisdom to come to the same place where the dragon race relies on the innate surface space knowledge and experience accumulation. Most of the formulas listed by Wang Qi are very intuitive for her, and they can be understood at a glance. However, the latter also made her feel a bit difficult-about equal to the last major question in the college entrance examination mathematics and the like?
The human race is similar to the dragon race in this respect, and even slightly more than a few points.
Yueluo Liuli voiced into the secret: "It's interesting to watch the drama."
Ao Liu also discovered the behavior of Yueluo Liuli. He was annoyed: "His Royal Highness is familiar with you. You know these things are normal. Let's say something else."
Wang Qi nodded: "OK"
"In contrast to the Sacred Ocean Geometry, there is another kind of geometry. Although the Sacred People are proficient, they have never taught us, and I think they should not ..."
Wang Qi grabbed the long sword beside him and waved forward. Everyone saw only a sword light. Afterwards, the walls made of ice were smoothed out and engraved with new text, and the ice chips rustled down. When Wang Qi blows gently, the room is as if there is light snow: "Okay, let's see. Is this what you asked? Is the content on it?"
The so-called "Sacred Ocean Geometry" is nothing but hyperbolic geometry-it is called Lobachevsky geometry on Earth. In the ocean, "sound" is a better information transmission medium than "light". Many marine creatures rely on "singing" to locate. The speed of sound transmission 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 organisms, the world "looks like" a concave sphere with a center in the sea. And this perception extends infinitely again, it becomes hyperbolic geometry.
In the words of the earth. According to what they heard, they lived on a Poincaré disc.
The oldest dragon family relies on sonar to perceive the world. Their innate sense of space is Roche geometry. And when they have a civilization and have developed methods, and learn to use their eyes, it is easy to discover European geometry. After knowing European geometry, discovering Lai's geometry is not too difficult.
This is how many marine species developed geometrically. They lag behind in "using fire", but they are compensated in this respect.
For races that rely on eyes only, the process is many times more difficult.
Austrian Liu just asked about the hyperbolic geometry-Roche geometry, and now it must be Li's geometry.
The successor of Shen Lanjiao was in a trance, feeling that his world view was challenged. He said: "In this geometry, there are infinite secrets of time and space ..."
Wang Qi was too lazy to laugh at her face. He added something behind his backhand with all knowledge points, that is, the use of Riemannian geometry in the theory of relativity, including Minkowski space. For Li's geometry, Wang Qi's cognition is even more profound, because this uses more in physics.
"I said, students of the Shenlanjiao family, would you like me to write a specific method to go up?"
Aoliu's face changed: "I can draw pictures and draw pictures, and the role of writing symbols is limited ... don't you say that mathematics is the study of computing? Let's compare one by one!"
He lifted the next formula by hand and then said: "Unlock this!"
Lucky in Austria ’s heart. Fortunately, one of his acquired teachers is also a member of the mathematics. There is a secret solution, which has broken the Tianyuan style listed by 33 demon aristocrats ...
This solution was all secretly secreted by his acquired teacher, little is known.
Just when he was distracted, Wang Qi had burned his conclusion with sword energy at his feet. Austrian Liu has not even recovered. He appalled: "So fast! It's impossible ..."
Wang Qi just took a glance and solved his formula, even shorter than the time he first set the value and then deduced the formula!
"You're surprised, but it's just triple Tianyuan [cubic equation]." Wang Qi said: "You have a higher level of ability?"
Au Liu's face was flushed. He pondered for half an hour, and Wang Qi was not in a hurry, so he waited so full. After that, he wrote another equation-the fourth degree equation.
Wang Qi still glanced and answered at will.
"If you make a five-fold Tianyuan [Five-time equation], I would look at you a bit higher." Wang Qi said: "What else is there, just let me have a look."
At the beginning, he really hoped that the other party could ask something he didn't know. Because it shows that the human race may not have realized the part of the field of non-European geometry-this part may be a blind spot formed by the difference of "innate spatial sense".
But now it seems ... haha.
As Austrian Liu grabbed a life-saving straw, he said, "There is no precise solution to the five-fold Tianyuan in your mouth."
"Hehe" Wang Qi rolled his eyes and said, "You guys, I hope you can get rid of the old ideas in your mind when studying with me. According to my original plan, I will teach you how to solve the fivefold next year. Tianyuan's ... the original plan. "
For a moment, Austrian wanted to let Wang Qi really solve a quintic equation. However, he did not speak out.
He has at least a little reason, knowing that Wang Qi will not be kidding about this matter. And after speaking out, his greatest possibility is still to insult himself-he may not understand the solution at all.
Wang Qi stared at Austrian Liu with some regrets at the end.
The fourth-order to fifth-order equation is actually a huge threshold. The first order quadratic equation and even most cubic equations can be solved in a very intuitive and very simple way. The biggest breakthrough here is probably the introduction of the concept of "imaginary number".
The square root of the negative number is unimaginable in the eyes of most ancient mathematicians.
After the fourth-order equation, the difficulty of the equation began to surge. The fourth-order equations are still easy to solve, but the fifth-order equations are completely impossible.
Even if you use pre-prepared numbers to make up the fifth degree equation, those numbers can only be used as one of the solutions of the fifth degree equation.
Many solutions of the quintic equation are nested and expressed, and this expression often contains many kinds of "symmetric operations".
Yes, symmetrical. At this point, "group theory" is needed to solve the equation. He is basically certain that it is incomprehensible to update the level of demon race arithmetic.
After all, the civilization of the updated demon race is not based on mathematics. They have a 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, is it not excessive?"
Aoliu was stunned and gritted his teeth: "If you press me with unsolved questions ..."
"Relax, you can't use unsolved problems yet. I can guarantee it is very simple. Among the human races, the basics of research and calculation are basically known.
Although Austrian Liu knew that Wang Qi was not well-intentioned, he nodded.
Wang Qi asked: "What is length? What is area? What is volume?"
If you like to walk into Xiuxian, please collect it: (EbookFREE.me) Entering Xiuxian's pen has the fastest literature update.
