175.

The 1000th floor is undoubtedly an extremely important floor.

Otherwise, the third-generation ancestor of Qingling Island, Guiyuan Zhenren, would not have put the inheritance of yin-yang arithmetic at this level.

And when Cheng Li sees the question on the 1000th floor now, he also has a feeling that it is indeed this question.

In fact, after he finished the previous 999th floor problem, he had a hunch that the 1000th floor would be this problem.

Because it's so classic, and it's so iconic.

From the previous 999 questions, Cheng Li also probably knew that this arithmetic tablet was randomly selected for himself this time, I don't know if it was because of coincidence or other special reasons, it was almost tailor-made for himself.

The entire question bank, starting from the first layer, is almost the historical process of the development of mathematics of human civilization on the earth.

Therefore, the first to the 500th floor is the part of ancient Chinese arithmetic, which dates from the 10th century BC to the end of the Yuan Dynasty in the 14th century AD.

Floors 501 to 999 are questions from the 400 years from the end of the Middle Ages to the Renaissance, that is, from the 13th century to the 16th century AD, in the development of European mathematics.

I don't know if it's a historical coincidence.

In the 14th century, when the development of mathematics in Chinese civilization began to decline, it happened to be the beginning of the European Renaissance.

In this way, under such a coincidence, history has alternated.

The development of mathematics in one civilization began to decline, and at the same time, the civilization of another system happened to be seamlessly connected in time and rose with it.

The alternating cycle of rise and fall in history is always full of many coincidences.

The problems on floors 501 to 999 contain many of the major mathematical classics of the European Renaissance.

For example, it includes solving cubic equations, solving quadratic equations, imaginary numbers, logarithms, etc.

Some questions also arise about the systematization of mathematical symbols.

One of the most significant signs of modern mathematics is the symbolic system, in which mathematical symbols are widely used, which reflects the high degree of abstraction and simplicity of mathematics.

And the systematization of mathematical symbols was also done during the Renaissance.

In addition to algebraic problems, there are many Renaissance geometry problems in floors 501 to 999.

For example, trigonometry, perspective, projective geometry.

In addition, there is a large part of the problem, which is about analytic geometry.

Modern mathematics can essentially be said to be the mathematics of variables.

And the first milestone in the mathematics of variables was the invention of analytic geometry.

Half of the 100 questions in Arithmetic Tablets 900-999 are related to analytic geometry, which shows its importance.

The basic idea of analytic geometry is to introduce the concept of "coordinates" into the plane, and then establish a one-to-one correspondence between the points on the plane and the ordered real numbers (x, y) with the help of coordinates. In this way, an algebraic equation can be mapped to a curve on a plane, so that the geometric problem can be reduced to an algebraic problem, and in turn new geometric results can be discovered through the study of the algebraic problem.

The establishment of analytic geometry originated from two famous mathematicians, Descartes and Fermat.

So 30 of the last 100 questions are from Descartes' Geometry and 20 are from Fermat's Introduction to the Trajectories of Planes and Three-Dimensionals.

Therefore, after completing the answers to questions 900-999, Cheng Li already had a strong premonition and knew what to ask in question 1000.

That's right, the 1000th level of the problem is related to calculus.

It is the most important content of high mathematics that tortures many college students to death - calculus.

"Hehe, it's really calculus...... Cheng Li said with an expression that I already knew this, "but it's not surprising that the establishment of calculus is a milestone in the history of human mathematics and even the history of scientific development on earth, and it is not an exaggeration to say that it is the beginning of modern human science." The problem of the 1000th layer is related to calculus, which is reasonable. ”

Cheng Li looked at the light words suspended in the center of the room on this floor, and composed a very classic question.

It reads:

"Featuring two or more objects A, B, C,...... At the same moment, draw the line segments x, y, z,...... Knowing the equations that represent the relationship between these line segments, find their velocities p,q,r,...... relationship. ”

When Cheng Li first saw this question, he knew its origin.

This is from Newton's "A Brief Theory of Flowing Numbers", and it is also the first paper in history to explicitly put forward the concept of calculus, although this "A Brief Theory of Flowing Numbers" was not officially published at the time, only circulated among colleagues, but in the end it is still recognized by most people as the first systematic calculus paper in history.

In A Brief Theory of the Number of Streams, Newton used calculus to calculate "the problem of the instantaneous velocity of an object at a certain moment." ”

As a former student of the mathematics department of the university, Cheng Li naturally knows the entire derivation process of calculus, so this 1000th layer problem is not difficult for him at all.

I saw Cheng Li stretch out his hand, and in that point of light, he began to write.

This is also a way to solve a problem, directly on the light curtain formed by the light point, and enter the answer by hand.

So Cheng Li wrote down Newton's derivation process of this problem in "A Brief Theory of Flowing Numbers".

"Known equation: X^3-abx+a^3-dyy=0......"

Next, after writing a series of proofs and derivations, Cheng Li wrote the final result of the problem: a formula, the fundamental theorem of calculus.

After writing down this fundamental theorem of calculus, the point of light floats again, and the word "correct" appears.

And this time, two roads appeared in front of Cheng Li.

One leads to a staircase to the next level, and the other leads to the depths of this level.

At this time, Xiao Shutong appeared in front of Cheng Li out of thin air, and after turning around in the air, he said to Cheng Li.

"Wow, I really didn't expect that a Qi Refining Stage cultivator like you would actually be able to break through to the 1000th layer, although it is said that it is some knowledge that you already know, but it is obvious that you also fully understand this knowledge, otherwise you would have been judged by the arithmetic tablet as a mistake and failed the trial. ”

Cheng Li didn't show any joyful expression, for him, the 1,000 floors were just the beginning.

Then he asked, "There are two paths here, I guess one leads to the next level, and the other leads to the inheritance of yin-yang arithmetic?"

Xiao Shutong praised: "That's right, you're quite smart." In addition, that one is indeed the inheritance of yin-yang arithmetic that leads to Qingling Island. You now have two options.

"1. Choose the path that leads to the inheritance of yin-yang arithmetic on Qingling Island. But your arithmetic tablet trial will also be over. ”

"2. Choose to continue to participate in the trial, but if you fail if you don't reach the 2000th level, you won't be able to obtain the Yin-Yang Arithmetic Inheritance.

In other words, only on the 1000th and 2000th floors can you obtain the inheritance of yin-yang arithmetic. Of course, if you can reach the 3000th floor, then you can become the master of the Arithmetic Monument, and at that time, you will naturally be able to enter and exit the Yin-Yang Arithmetic Inheritance at will. ”

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(In the last few chapters on the history of mathematics, Rabbit has looked up a lot of materials on the history of mathematics on the Internet.)

I also bought some books to refer to, such as "Introduction to the History of Mathematics" by Li Wenlin, and "The Wonderful History of Mathematics" by Joel Levy, which I would like to explain.

Rabbits will strive for rigorous and truthful sources, and will not make things up, which is also the consistent style of rabbits. ）