Future library

Starting from the first year of high school, many students will wonder why we should learn parabolas and why we should start with this weird thing.

In China, 90% of students will never know the answer from birth to death. Some people may not even think about it, while others may have thought about it and asked about it but did not get a satisfactory answer. As a result, generations of Chinese students studied parabolas with their minds full of doubts, thinking that it was the simplest graph in the world.

It is certainly not the simplest figure in the world. It is surprisingly difficult and consumes countless genius brain cells. It has only been studied by too many people and appears to be simple.

The reason why students start learning parabolas is to learn conic sections. From circles, parabolas, ellipses to hyperbolas - all high school mathematics content - all talk about the same problem: conic sections.

Descartes's research is perhaps the main culprit that brought conic sections into all schools. In his coordinate system, the image of a quadratic equation can represent conic sections, and all conic sections are derived in this way, thus making geometry Close connection with algebra. However, not all coordinate systems can do this. Scholars just chose the simplest and most orthodox way and put it in textbooks.

The orthodox and simple education model makes sense in many cases, such as for Chuanchuan people.

Even if he cheated in all exams, Cheng Jinzhou could still tell the properties of dozens or hundreds of conic sections without taking a breath, but he obviously couldn't do this.

Cheng Jinzhou turned around and read the content on the whiteboard carefully, pretending to think, but in fact he was judging the depth of the research of several star warlocks.

The earliest research on conic sections was about a little later than Euclid, and it was also before 200 BC. Then, like Euclidean geometry, it fell into silence for more than 1,000 years, then revived, then died, and then died. Immediately he faked his death, and was finally completely raped by Descartes...

As a necessity before analytic geometry, conic sections were also fully studied in the Great Xia Dynasty, especially the application of ellipses in astronomy, which was almost fatal to astrologers. Cheng Jinzhou said while making judgment: "I think the research on ellipses is very sufficient and is an important part."

Liu Kuang showed a very pious look and said: "Since Gao Muen's five-star warlock, the flexibility of the star warlocks in the air has been greatly improved. Now the star warlocks who can fight in the sky have unique research on ellipses. Of course, The triangle is also an indispensable part.”

Cheng Jinzhou was speechless after hearing this. A five-star warlock requires 100,000 Covenant points, which is equivalent to 100,000 people using his research results. This is definitely an amazing achievement. In the entire decade after the 21st century, the most cited single paper (Note 1) was an American chemistry paper, which was cited only more than 7,000 times. In the past 10 years, the number of citations of all Chinese papers was It is only more than 2.6 million times. Considering the speed and quantity of papers published in modern society, as well as the sparse number of astromancers, it is not an exaggeration to call it great.

Looking at Lu Xu again, he looked convinced. This five-star warlock Gao Mu'en was probably a well-known legend. Cheng Jinzhou didn't want to ask him for details to avoid revealing his secrets. Instead, he pretended to understand, organized some words, and said He spoke slowly: "About the ellipse, I know that it uses a plane perpendicular to the cone axis to truncate the cone, and the result is a circle. If the plane is gradually tilted, the result is an ellipse. It also has a focus... Well, it should be possible to use the formula Express."

He spoke deliberately hesitantly, as if he was talking about an area he was not familiar with.

"Do you know how to make a focus? And the formula for an ellipse?"

"I just know some specific contents..." Cheng Jinzhou spread his hands and smiled sheepishly.

Liu Kuang's question is certainly not difficult, but the conceptual formula must be simplified and special, and may not be exactly the same as what the star warlocks understand. Just like Euclidean geometry, the conic sections and theorems and formulas that high school students learn were obtained after more than a thousand years of improvement. It is natural to have different expression methods.

Although it was just two simple sentences, Liu Kuang nodded with satisfaction and said: "It is indeed not easy to go from plane geometry to dynamic geometry. This shows that you are also very serious about your studies. Do you have any books to read now?" Case?"

The books of Star Warlocks are still circulated among the nobles, but they are never comprehensive and rich.

Cheng Jinzhou was 10. He used to say that he was self-study, but he did not prepare relevant books. Fortunately, Liu Kuang didn't care, otherwise it would be another trouble.

Not wanting to talk about something that could easily reveal his flaws, he just nodded quickly and said, "It's okay, so I can take your airship? When will it leave?"

"When do you want to set off?" Wang Linghe smiled kindly.

"It's best to arrive in the capital within half a month."

If it is a fast carriage, it will take about 20 days to reach the capital. As the saying goes, the nights are long and the dreams are many, so it is better to arrive earlier.

"Then let's set off the day after tomorrow. We've been gone long enough." Liu Kuang agreed and came down, flexing his fingers and saw an attendant walking over with a stack of books in his arms.

There are four books in total, all of which are hand-copied, but the paper is very good and the white color is far better than what can be bought in bookstores. It looks more like a printed book from the Republic of China period, which was definitely a rarity in the Great Xia Dynasty.

"The four books are all about ellipses and parabolas." Liu Kuang took the book in his hand and passed it to Cheng Jinzhou: "If you are sure about the imperial examination, read more books about star warlocks."

At any time on this planet, the number of star warlocks is limited, and there are even fewer star warlocks who can develop in theory. When Liu Kuang determined Cheng Jinzhou's potential, some overtures were inevitable. This is true for air tickets, gift books, and airship rides.

Cheng Jinzhou opened the book politely, and it turned out to be a standard essay format. Such a book must be extremely boring. He has been forced to read by his parents since he was in college. Unexpectedly, he came to another world to be no exception. Of course, the content in the book is very useful. At least you can have a systematic understanding of the research on conic sections in the Great Xia Dynasty. In addition, you can also remember many symbolic applications. However, after holding up four books with the momentum of a lazy person, Cheng Jinzhou's scalp felt numb again.

When reading such books, it seems that I always have to describe them as chewing.

"Let's continue. You can read and listen." Liu Kuang stood up with a smile and returned to the whiteboard. The same is true for Wang Linghe and Xiang Xin.

Cheng Jinzhou's eyes widened, wondering when he had fallen into the group of hard-working people again.

The wind was blowing in the sky above the courtyard. The courtyard was still as warm as spring, and the atmosphere inside was surprisingly harmonious. Cheng Jinzhou was a little afraid to face his parents' sadness, so he simply didn't say goodbye and just half read a book and half watched the crowd writing and drawing on the whiteboard.

Xiang Xin and Liu Kuang have a master-disciple relationship, and Wang Linghe is Liu Kuang's junior brother. The three of them were talking and writing on the whiteboard. The discussion was very much like a brainstorming session in later generations, with Liu Kuang taking the lead and also being able to Taking advantage of the strengths of the other two people opened Cheng Jinzhou's horizons. In the academic world he knows, such face-to-face discussions are rare. It is becoming increasingly difficult for researchers to break away from computers, and computers are becoming larger and larger. Even for theoretical physics, it is difficult for people to use two Use a blank piece of paper to express your thoughts. In international and domestic meetings, participants often have to prepare carefully for dozens of days before they can describe it as clearly as possible. In fact, most scientists who participate in meetings still mainly read the meeting minutes, and few can understand everything on the spot.

Cheng Jinzhou did not participate in it, but listened quietly, pretending to have only a half-knowledge of conic sections, which greatly pleased Warlock Xiang Xinxing. With the qualifications of a first-level star warlock, being educated by a young boy all day long, even if he acknowledges his talent, he will still feel depressed occasionally.

Lu Xu, like Cheng Jinzhou, held a tea cup and just listened. He is a pure combat star warlock - the burden of star arrays on the human body is very heavy, and only a few people can etch more than 4 star arrays. For such people, the requirements will naturally be lowered accordingly.

However, in Cheng Jinzhou's view, the requirements for Mr. Lu Xu were so low that he could not even reach the level of ordinary people. The star array he used was completely designed for combat. Compared with serious star warlocks, It's quite flexible and changeable.

Just when Cheng Jinzhou turned his attention to the whiteboard, the customer service man jumped out without warning and said seriously: "There are still 24 hours until the end of the loan period. If you fail to repay after the deadline, the mortgage contribution points will be deducted." Under the premise, the principal will be recovered.”

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Note 1: The number of citations in a paper refers to when someone publishes a new paper and directly uses the conclusions of the paper. It is equivalent to acknowledging the results of the paper and indicating that it is influential and useful in the field. At the same time, there are certain requirements for the journals in which the cited papers are published.

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