Future library

Use ruler and compass to draw and complete a regular heptagon!

Before anyone else could say anything, Cheng Jinzhou was stunned on the spot.

He swears by the doctorate he got through the back door that this kind of topic was definitely not thought up by the old lady herself.

Don't think that making a regular heptagon is easy. Before the 18th century, this was a world-class problem, and it was a very meaningful topic.

These days, Cheng Jinzhou is reading books about geometry every day. Although there are not many such books at home, he can also learn about the mathematical level of the world from the side.

It may be able to reach the level of Europe in the early 16th century, and it may still be able to surpass it in some aspects, but studying how to make a regular heptadagon - to some extent, has surpassed the limits of this era. .

The so-called ruler and compass drawing is a method of drawing figures using rulers and compasses without graduations only for a limited number of times. The limited number of times mentioned here eliminates the use of trial methods.

This is a proposition that seems simple but is actually complex. In fact, in the history that Cheng Jinzhou spent, this proposition was finally solved by Gauss - another amazing mathematical master. His contributions in his life were numerous, including the least squares method, which caused headaches for science and engineering students. As well as the normal distribution curve that he often comes into contact with liberal arts students, are all his achievements. As for the most familiar thing about Lord Gauss's wisdom, perhaps it is the calculation problem he completed when he was ten or nine years old: 1+2+3+...+100.

In the 21st century, children who have been exposed to the Mathematical Olympiad may not know Gauss, but when you ask "How much does it add from 1 to 100?", most people may not even do the math and just look up and answer: "5050."

When Gauss entered university, he began to study how to solve the regular heptadagon using rulers and compasses. Cheng Jinzhou had long forgotten how long it took, but it naturally took longer than 20 minutes. In other words, unless the star warlocks of the Great Xia Dynasty It would be absolutely impossible to advance the level of mathematics for more than 100 years.

Mathematics is a step-by-step process, truly building a fortress in the sand. It can be unique, but it can never develop by leaps and bounds - a mathematical formula that lacks a one-step proof is wrong.

Cheng Jinzhou believed that if the astrologers of the Great Xia Dynasty could generally understand the heptadagonal ruler and compass construction method and the propositions related to it, then they would have entered the industrial society long ago - this is obviously impossible.

At this time, there is no point in 20 minutes. The old lady should be prepared to let the two children not answer the questions.

This is a good way, it won't ruin Long Zizhi's face too much, and it can be regarded as a safe win. The only problem is that Cheng Jinzhou is a little unhappy.

If the old lady hadn't been so shrewd and had to compete in math with a big kid, Cheng Jinzhou would still be very, very confident.

Even a Physics Ph.D. produced by cheating will never be weaker than a 16th century high school student.

In fact, even if he had to draw a regular heptadagon, Cheng Jinzhou could undoubtedly complete it within 20 minutes.

Studying how to draw a regular heptadagon and its principles, even in modern times, can be used as a graduation thesis for undergraduates in the Department of Mathematics, but using the method developed to draw a ruler and compass is a midterm exam for first-year junior high school students. .

The problem is that in the eyes of everyone, Cheng Jinzhou does not seem to have the ability to transcend the times.

Dr. Cheng himself was not similarly prepared.

Time passed minute by minute.

His opponent Cheng Jinhao leaned on the table early and tried to come up with an approximate pattern of a regular heptagon. At the level of a 14-year-old child, he obviously did not expect how difficult the problem would be - it required mathematics. The elites have accumulated 200 years of strength before they have the opportunity to succeed. There are too many formulas, theorems and ideas, and we have to rely on predecessors to create and summarize them.

Cheng Jinzhou knew, so he simply stood aside and looked at everyone with a joking expression.

The members of the Cheng family can be said to be the most educated elite group in the world. Each of them has received nine years of compulsory education in the famous Cheng family private school. However, when faced with a problem that transcends 200 years of knowledge, they He is no different from 14-year-old Cheng Jinhao.

Most people pointed at Cheng Jinzhou and then at Cheng Jinhao with expressions that showed they had known this before. Obviously, a child who lies down to answer questions is more convincing than a child who gives up on his own initiative.

Cheng Jinzhou was very dissatisfied with the different expressions on the onlookers' faces.

Especially when the men in black robes also used their eyes to locate the "second ancestor who didn't work hard", Cheng Jinzhou was furious.

As a former active doctor, Cheng Jinzhou hates people looking at him as a "second-generation ancestor who doesn't work hard", even though he has indeed cheated countless times and is indeed a dishonorable second-generation ancestor...

No need to look at the expressions of Cheng's mother and Cheng's father, Cheng Jinzhou stood up impulsively, pointed at the black robes and said, "Can you do it again?"

"Cheng Jinzhou!" Cheng's father was stunned, and then he became angry with a face full of anger.

It's true that the black robes don't even have a one-star rating, but they have the potential to become real star warlocks. In places like the Great Xia Dynasty, they were also recognized as star warlocks. Astromancers deserve to be respected everywhere, at least not to be scolded by a child.

Cheng Jinzhou did not back down. He has never been a very rational person. He pointed his thin fingers from left to right and said, "You have been immersed in astrology for many years, but now you can answer this question? What's the point?" Are you qualified to laugh at me?"

The words are a bit harsh, but in terms of mathematics, Cheng Jinzhou can indeed be proud of the star warlocks worshiped by the Cheng family. He said proudly: "There is currently no solution to this problem. Am I right?"

The polite questioning made the scene quiet for a while. Magistrate Cheng didn't say anything when he saw the old lady, so he simply didn't say a word.

The star warlock who had asked the first question continued to stroke his beard and said nonchalantly: "I, Wu Zong, can't answer this question."

With good demeanor and noble status, everyone immediately recognized him, and they all said "no problem" and started a heated discussion. This is obviously another topic worthy of showing off at the dinner table.

Cheng Jinzhou was not an economical person, not before, and even less so now. Taking advantage of his young age, he waggled his fingers and said: "Mr. Wu, you haven't answered my question yet. Not only can you not answer this question, but there is no star warlock." You can answer it, right?"

"This..." Wu Zong stroked his beard and was speechless for a moment. It seemed not easy for him to admit the Star Warlock's failure.

Perhaps he was really too young, but Cheng's father, who was mature and prudent, did not stop his son and stood aside to watch his performance. As a prefect, he rarely got along with his growing son from the day he took office. I also want to see how much knowledge the children who have been on the sickbed all year round have learned and how much they have to do with others.

Cheng Jinzhou did not hesitate and turned to the old lady: "Grandma, I know that there is no solution to this problem at the moment, but Cheng Jinhao doesn't know it. From this point of view, although neither of us has completed it, I know more." Some, isn’t it?”

The philanthropic Cheng Bingxun spoke without restraint and immediately said: "Cheng Jinhao worked hard to complete the inspection, but you rely on a little knowledge and cleverness to try to win. You should be considered a loser."

The legitimate son of a dignified clan, it was already embarrassing to interfere in the younger generation's game, and now he went into battle shirtless. Not to mention the people of the Longzi clan, other members of the Cheng family couldn't stand it. Someone behind him suddenly muttered: "Cheng Bingxun is kind and generous, and Cheng Bingxun is free of money. Officials are as pure as water, Cheng Bingxun..."

There were a lot of names, many of which were heard by Cheng Jinzhou for the first time. He almost laughed out loud, but he restrained himself after thinking about the gift of Ba Qing.

The old lady didn't answer Cheng Jinzhou's question, but smiled gracefully and said in a friendly manner: "Since neither of them can answer the question, and the previous question, it's better for Jinzhou to enter. After all, he is the legitimate grandson."

"After all, he is his legitimate grandson", these words made the philanthropic gentleman's face turn blue and red.

Cheng Jinhao is also a legitimate grandson, but the word "long" is a little farther away. If it weren't for his good father, the old lady would not have said that. Now, the father and son can only experience the hierarchical society cruelly.

With such an arrangement, Cheng Bingxun couldn't make any excuses. He watched Cheng Jinzhou answer and watched Cheng Jinzhou get up and walk out, praying with all his heart.

This small episode left the Cheng family with nothing more than a source of conversation, and it quickly dispersed, leaving only households with children waiting to be tainted by the joy of the ceremony.

Cheng Jinzhou strode into the bright long house.