Into the Immortal Cultivation

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"The demon emperor Tai Yi has cattle grazing in hibiscus, and its color is four-quarters. It is black and white, brown and yellow, and there is a difference between black and white. The number of white cattle is the number of brown cattle plus half of black cattle, plus The number of black cattle is one third. The number of black cattle is one quarter of the number of yellow cattle, plus one fifth of the number of yellow cattle, and the number of brown cattle is white. The number of yellow cattle is white. One-sixth of the number of bulls, plus one-seventh of the number of white bulls, plus the number of brown bulls. Re-discuss the number of stags, white stags, which is one-third of the number of blacks, plus The number of black cows is one-quarter. The number of black bulls is one-fourth of the number of yellow cattle, plus one-fifth of the number of yellow cattle. The number of brown ox is one-sixth of the number of white cattle. Add one-seventh of the number of white cows. And ask the demon emperor's cow, what is the geometry? Another question, if the black and white stag array is just a positive moment, the brown-yellow stag array can be a triangle, and then ask, black and white Does brownish yellow scorpion each have geometry? "

After Chiron slowly reported the problem, he looked at Wang Qi slightly proudly. When he returned the stunned expression on Wang Qi's face, he was somewhat worried.

He is very optimistic about this younger generation, not only because he waited for 50,000 years to wait for such a suitable inheritor, but also because Wang Qi has several inheritances and mathematical precepts.

This is the condition, the unspeakable condition.

What if he ca n’t answer? Do you want to give a hint?

When Zhilong lived to think so, Wang Qi only felt absurd.

This is ... an ancient puzzle?

Well, this is indeed a problem. The problem of the Archimedes herd, the great mathematician Archimedes has studied a problem that has not been solved for a long time.

However, no matter how difficult the problem is, it is also time-limited. Before the invention of calculus, the irregular shape can only be measured by using the patching method, which is extremely troublesome and unpredictable, but after the emergence of calculus, such world problems are just general exercises. Earlier, in the era when the yuan-changing method was not born, binary equations were a problem that could make big mathematicians scratch their heads. There was once a mathematician on earth who hated another mathematician who stole the solution of the equations and went to the Inquisition to frame the other party as a wizard.

The advancement of mathematical tools and means of seeking for the road has gradually reduced the difficulty of the previous problems.

The reason why primary school Olympiads can stump college teachers is also because these kinds of problems often limit the mathematical tools. Equations and calculus are not allowed. They simply make a simple problem difficult.

"The biggest problem in this question is the amount of calculation ..." Wang Qi sighed and directly reported the answer: "This question has infinite solutions. The first question has the smallest solution of 5916837175686 heads, and the second question has the smallest number of solutions that exceeds two. There are more than one hundred sixty-five thousand people who have to answer for a few hours with their mouths. Senior, let ’s write it ... "

"Impossible! This is impossible!" Zhilong's expression was horrified, as if he saw the most incredible thing in the world.

He was ... he actually ... he actually reported the answer directly?

"Someone must have made this question in the past 50,000 years. Did you remember it?" Zhilong found a reason to calm down. But Wang Qi felt that the other party was a little bit fierce. He listed a few equations on the ground: "So that real people know that in the ancient times, I had another breakthrough in my ancestors, and I got a new learning, the name" Tianyuan formula ". ... "

Zhilong doubted: "Elementary algebra?"

"That is, the algebra developed by the mathematicians in the Middle Ages is different from the new generation of mathematics developed by generations of my predecessors, and is called elementary. By the way, even Zongzong also absorbs this aspect." Wang Qi continued to explain : "Here we can list a four yuan Tianyuan group ..."

Zhilong felt that things were beyond his expectations. He hurriedly stopped: "Wait a minute, how does Lianzong absorb Lizong at all?"

Algebra is closely related to number theory, and it is naturally the root of alienation.

Wang Qi had to explain: "Predecessors once wanted to unify Lizong Lianzong and create a new one, called" The Law of Heaven "..."

The so-called celestial law naturally refers to the basis of celestial power, analytical geometry.

Analytical geometry appeared very early, and Zhilong did not understand it difficult. However, it was precisely because he was understandable that he felt even more shocked in his heart: "This ... Wushuang Magic Method! This is the Tao! This is the Tao!"

Seeing Zhilong dance like a real person, Wang Qi couldn't bear it. The gap between them is not the gap of individual level, but the gap of civilization development. Excluding the ancient law period of nearly 50,000 years, the gap between them is the history of mathematics development in two thousand years!

If you want to use your own power to shake thousands of talents of thousands of years, it is difficult!

In a flash, Wang Qi listed several equations of one-element linear equations. Then the formulas for the number of squares and triangles are listed, and two binary quadratic equations are solved.

"The celestial law is formed according to the Euclidean law, and to calculate the eight-element tianyuan group, there must be eight two-two vertical number axes ..."

Zhilong is going crazy: "Eight ... how could there be eight straight lines that intersect each other at one point?"

"Oh, this is an extension of Ou Taiyu, called 'Xianyu'. The ordinary space only has three directions of up, down, left and right, and front and back, which is three-phase. And 'Xianyu' has infinite phase ... … "

"What's the use?"

"Uh ... on a normal scale, there is no use of eggs, but this is necessary to study the micro world or complex systems ..."

The more Zhilong real people asked, the more maddening his expression was. But when Wang Qi solved the problem, he had calmed down.

The middle-aged mathematician sighed: "Awesome for later generations, awesome for later generations!"

"The Yangtze River ... cough and cough, the big waves are pushing forward, and one wave is stronger than the other." Wang Qizheng said: "This is a slang in my hometown."

Zhilong lively laughed: "A good one wave is stronger than a wave! This sentence is good! Tasteful!" Immediately, he stared at Wang Qi with burning eyes: "I still have a few questions here ... No, it's not about you. I know, I can't test you anymore. I just want to know if these problems will be solved in future generations. "

Wang Qi nodded: "Okay."

"Purely drawing on rules, can you solve the three problems of cubic product, turning circle into square, and trisection angle?"

Rule drawing, also called ruler drawing on the earth, is simply a method of drawing a drawing with compasses and rulers without scales. Cubic product, that is, to find the side of a cube, so that the volume of the cube is twice that of a given cube; turning a circle into a square, that is, to make a square, making it equal to the area of ​​a given circle; three equal parts The angle, that is, a given arbitrary angle is divided into three equal parts.

Wang Qi shook his head and said: "It's impossible. First, turning a circle into a square will involve a number, that is, the ratio of pi and the diameter of the circle. And we can use arithmetic to prove that pi is a transcendental number-what is The number of transcendences will be asked later. In short, I will say one thing first. This transcendence number is absolutely impossible to do with a simple compass rule. Cubes are difficult to be explained by product. First, let ’s talk about a few concepts. This concept comes from Yu Gaoxiang's general solution to the Tianyuan formula ... This problem can be transformed into a group theory problem ... "

Galois theory, one of the important theories of group theory.

Zhen Jiezi has listened to more courses for more than half a year than Zhilong, but his acceptance ability is not as good as that of a middle-aged mathematician. He just thought this scene was a bit absurd.

Said the test, as if ... became a lecture?

And is the subject being taught by the subject?

This ... is crazy!

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