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Chapter 67 Conic Sections

From the beginning of high school, many students will wonder why we should learn parabola and why we should start with this strange thing.

In China, 90% of students will not know the answer from life to death. Some people may not think about it, while others may think about it but fail to get a satisfactory answer. So, generations of Chinese students learn parabolas with confusion, thinking that this is the simplest figure in the world.

Of course it is not the simplest figure in the world. It is surprisingly difficult. It consumes countless genius brain cells. It is just a simple matter that has been studied too much.

The reason why students start from parabola is to learn conical curves, from circles, parabolas, ellipses and all the hyperbolas - all the high school mathematics content - is talking about the same problem: conical curves.

Descartes' research may be the culprit that prompted conic curves to enter all schools. In his coordinate system, images of binary quadratic equations can represent conic curves, and all conic curves are drawn in this way, thus making geometry and algebra closely related. However, not all coordinate systems can do this. Scholars only chose the simplest and most orthodox way and placed it in textbooks.

Orthodox and simple educational models are meaningful in many cases, such as for traveling through time.

Even though cheating was used in all exams, Cheng Jinzhou could still tell the characteristics of dozens or hundreds of conic curves without breathing, but he obviously could not do so.

Cheng Jinzhou turned around, looked carefully at the content on the whiteboard, pretending to be thinking, and in essence he was judging the depth of research of several astrology warlocks.

The earliest study of conic curves was about a little later than Euclid, and it happened 200 years ago. Then, like Euclidean geometry, it fell into silence for more than 1,000 years, then recovered, then died, then pretended to die, and then pretended to die, and finally was completely* by Descartes...

As a necessity before analyzing geometry, conical curves were also well studied in the Daxia Dynasty, especially the application of ellipses in astronomy, which was almost fatal to astrology. Cheng Jinzhou said while making a judgment: "I think the research on ellipses is very well-researched and an important part."

Liu Kuang showed a very pious look and said: "Since the five-star sorcerer of Takamuen, the flexibility of the astrology sorcerers in the air has greatly improved. Now the astrology sorcerers who can fight in the sky have unique research on ellipses. Of course, triangles are also indispensable content."

Cheng Jinzhou was very upset. The five-star sorcerer required 100,000 star covenant points, which was equivalent to 100,000 people using his research results, which was definitely an amazing achievement. In the entire decade after the 21st century, a single paper was cited the most (Note 1) was an American chemistry paper, which was cited more than 7,000 times, and the number of papers in China in the past 10 years has been cited only more than 2.6 million times. Considering the speed and number of papers published in modern society, as well as the rare number of astrology warriors, it is not an exaggeration to call it great.

Looking at Lu Xu, he looked convinced. This five-star sorcerer Gao Muen is probably a well-known legend. Cheng Jinzhou couldn't ask for details anymore to avoid revealing it. Instead, he pretended to understand, organized some language, and slowed down his speech: "About the ellipse, I know that it uses a plane perpendicular to the cone axis to cut the cone. What he got is a circle, and the plane gradually tilted, and what he got was an ellipse, and it also had a focus... uh, it should be expressed in a formula."

He deliberately said hesitantly, as if he was talking about a field that he was not familiar with.

"Do you know how to do focus? And the formula expression of the ellipse?"

"I just know some specific content..." Cheng Jinzhou spread his hands and smiled embarrassedly.

Of course, Liu Kuang’s problem is not difficult, but conceptual formulas must be simplified, special, and not necessarily exactly the same as what astrology masters know. Just like Euclidean geometry, the conic curves learned by high school students and the theorem formulas learned were all obtained after more than a thousand years of improvement. It is natural to have different expression methods.

Although it was just a few 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 reading. Will there be any situations in reading books now?"

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

Cheng Jinzhou is 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 things that are easy to show off, he just nodded quickly and said, "It's okay, so I can take your airship? When will I set off?"

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

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

If it is a fast carriage, it will take about 20 days to arrive in the capital. As the saying goes, long nights and many dreams, it is better to get early.

"Then let's set off on the next day. We've been away for a long time." Liu Kuang agreed, hooked his fingers outside, and saw a servant walking over with a stack of books.

There are four books in total, all of which are hand-written versions, but the paper is very good, and the white color is far more than the goods you can buy in bookstores. It looks more like a printed copy from the Republic of China period, and was definitely a rare product in the Daxia Dynasty.

"The four books are all about ellipses and parabolas." Liu Kuang held the book in his hand and handed it to Cheng Jinzhou and said: "If you are sure of the imperial examination, please read more books about the astrology warlocks."

At any time on this planet, astral warriors are limited, and there are very few astral warriors who can develop in theory. When Liu Kuang determined the potential of Cheng Jinzhou, some kind of show of kindness was inevitable, such as flying tickets, gift books and flying boats.

Cheng Jinzhou politely opened the book, which turned out to be a standard paper model. Such books must be boring and flying. Since he went to college, he was forced to read by his parents, but he did not expect to come to another world. Of course, the content in the book is very useful, at least it can have a systematic understanding of the research on conic curves in the Daxia Dynasty, and can also remember many symbolic applications. However, with the aura of a lazy person, Cheng Jinzhou felt numb again.

When reading such books, it seems that they should always be described as chewing.

"Let's go on, you can read the book, you can also 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 widened his eyes, not understanding when he fell into the group of hardworking and hardworking people again.

The wind was blowing over the yard, and the yard was still as warm as spring, and the atmosphere inside was surprisingly harmonious. Cheng Jinzhou was a little afraid to face the sadness of his parents, so he simply didn't say goodbye, just reading books and half watching the crowd writing and painting on the whiteboard.

Xiang Xin and Liu Kuang are master-apprentice relationships, and Wang Linghe is Liu Kuang's junior brother. The three of them are on the whiteboard, talking and writing. The discussion is very similar to the brainstorm of later generations. They focus on Liu Kuang and can play the strengths of the other two, which has opened Cheng Jinzhou's eyes. In the academic world he knows, there are few such face-to-face discussions, and it is becoming increasingly difficult for researchers to get rid of computers, and the size of computers is getting bigger and bigger. Even in theoretical physics, it is difficult for people to express their thoughts with two blank sheets of paper. In international and domestic conferences, participants often have to prepare carefully for dozens of days before they can describe clearly. In fact, most scientists attending the conference still focus on reading the meeting minutes, and few people can understand clearly on the spot.

Cheng Jinzhou did not participate in it, but listened quietly and pretended to have a slight understanding of the conic curve, which made Xiang Xin a Star Warlock very happy. With the qualifications of a first-class star warlock, he was educated by a young boy all day long. Even if he recognized the other party's talent, he would still feel depressed occasionally.

Like Cheng Jinzhou, Lu Xu held a teacup and listened only. He was a pure combat star sorcerer. The star array had a very heavy burden on the human body. Only a few people could etch more than 4 star arrays. For such people, the requirements would naturally be reduced accordingly.

However, in Cheng Jinzhou's opinion, the requirements for Mr. Lu Xu were reduced too low, so that he could not even reach the level of an ordinary person. The star array he used was completely designed for combat, which was quite inferior to the flexibility and changeability of a serious astral sorcerer.

Just as Cheng Jinzhou turned his attention to the whiteboard, the customer service jumped out without warning and said seriously: "The loan period is still 24 hours before it is closed. If you don't pay it back within the deadline, you will recover the principal under the premise of deducting the mortgage contribution point."

...

Note 1: The number of citations in a paper refers to the conclusions of the paper being directly used when someone publishes a new paper. This is equivalent to acknowledging the results of the paper and indicating that it is influential and useful in this field. At the same time, there are certain requirements for the publication of the paper that cited the paper.

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