future library.

Chapter 59 Conics
From the first year of high school, many students will wonder why we should learn parabola 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.

Of course, it is not the easiest graph in the world, it is surprisingly difficult, it consumes the brain cells of countless geniuses, it is only simple because it has been studied too much.

The reason why students learn parabola is to learn conic section, from circle, parabola, ellipse to hyperbola - all high school mathematics content - all are talking about the same problem: conic section.

Descartes' work is perhaps the chief culprit that drives conics into all schools. In his coordinate system conics can be represented by images of quadratic equations in two variables, and all conics are derived in this way, so that geometry There is a close connection with algebra.However, not all coordinate systems can do this. Scholars just choose 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 though cheating was used in all the exams, Cheng Jinzhou could still name dozens or hundreds of properties of conic sections without panting, but he obviously couldn't do that.

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 conic curve research 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 1000 years, and then recovered, then died, and then cheated. Immediately suspended animation, and finally was completely raped by Descartes...

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

Liu Kuang showed a very pious look and said: "Since the five-star warlock Gao Muen, the astro-warlocks have greatly improved their flexibility in the air. Now the astro-warlocks who can fight in the sky have unique research on ellipses. Of course, Triangle is also indispensable.”

Cheng Jinzhou couldn't stop talking when he heard it.A five-star warlock requires 10 Star Alliance points, which is equivalent to 10 people using his research results. This is definitely a remarkable achievement.In the entire ten years after the 21st century, the most cited single paper (Note 1) was an American chemical paper, which was cited more than 7000 times, while the number of citations of all Chinese papers in the past 10 years There are only more than 260 million times, and considering the speed and quantity of papers published in modern society, as well as the rare number of astrologers, it is not an exaggeration to call it great.

Looking at Lu Xu's expression of admiration, this Gao Muen five-star warlock is probably a well-known legendary figure, and Cheng Jinzhou couldn't help but ask him for details so as not to reveal his secrets. Instead, he pretended to understand, organized his words, and let go 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, and gradually tilting the plane, the result is an ellipse, which has a focal point... Uh, 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 do the focal point? And the formula expression of the ellipse?"

"I just know something, the specific content..." Cheng Jinzhou spread his hands and smiled embarrassedly.

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 astrologists understand.Just like Euclidean geometry, the conic sections and the theorems and formulas learned by high school students were obtained after more than 1000 years of improvement, and it is natural to have different ways of expressing them.

Although it was just a few simple sentences, Liu Kuang nodded his head in satisfaction and said, "It is indeed not easy to go from plane geometry to dynamic geometry. Case?"

The books of astrologers are still circulated among the nobles, but they will never be comprehensive and rich.

Cheng Jinzhou is 0. He used to say that he was self-study, but he didn't prepare relevant books. Fortunately, Liu Kuang didn't care, otherwise it would be another trouble.

Not wanting to talk about things that would be easy to show his feet, he just nodded quickly and said: "It's okay, so I can take your airship? When are you going to leave?"

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

"It's best to reach 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 leave on the day after tomorrow, we've been away long enough." Liu Kuang agreed, and hooked his fingers outward, and saw a servant walking over with a stack of books.

There are four books in total, all of which are hand-copied, but the paper is very good, and the white color far surpasses the ones that can be bought in bookstores. It looks more like a printed copy from the Republic of China period, which is definitely a rare commodity 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. The same is true for flying 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.

Reading such books, it seems that it will always be described as gnawing.

"Let's continue, you can read the book, or listen to it." 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, not knowing when he fell into the group of hardworking people again.

There was a whistling wind blowing over the courtyard, the courtyard was still as warm as spring, and the atmosphere inside was surprisingly harmonious.Cheng Jinzhou didn't dare to face his parents' sadness, so he didn't say goodbye at all, half reading, half watching the crowd waiting to write and draw on the whiteboard.

Xiang Xin and Liu Kuang have a master-student relationship, and Wang Linghe is Liu Kuang's younger brother. The three of them are sitting on the whiteboard, talking and writing. The discussion is very similar to the brainstorming of later generations. Making use of the strengths of the other two opened Cheng Jinzhou's horizons.In the academic world he knows, such face-to-face discussions are rare. It is becoming more and more difficult for researchers to leave the computer, and the size of the computer is getting bigger and bigger. Even in theoretical physics, it is difficult for people to use two In international and domestic meetings, participants often have to prepare carefully for dozens of days before they can describe as clearly as possible.In fact, most of the scientists who participated in the meeting still mainly read the minutes of the meeting, and few of them could understand it thoroughly on the spot.

Cheng Jinzhou did not participate in it, but listened quietly, pretending to have a half-knowledge about conic sections, which greatly refreshed Warlock Xiang Xinxing.With the qualifications of a first-level star warlock, being taught by a young boy all day long, even if he admits the other party's talent, there will still be occasional depression.

Like Cheng Jinzhou, Lu Xu held a teacup and just listened.He is a pure combat astromancer - the star array is very burdensome to the human body, only a very small number of 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 are so low that he can't even reach the level of ordinary people. The star array he uses is completely designed for combat. It's not as flexible as it is.

Just when Cheng Jinzhou turned his attention to the whiteboard, Mr. Customer Service jumped out without warning, and said solemnly: "There is still 24 hours before the end of the loan period. Under the premise, recover the principal.”

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Note 1: The number of citations in a paper refers to when someone publishes a new paper, the conclusion of the paper is directly used.It is tantamount to acknowledging the achievements of the paper and explaining that it is influential and useful in this field.At the same time, there are certain requirements for the journals in which the cited papers are published.

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(End of this chapter)