I Just Want to Be a Quiet Top Student

"The last question, the last question left."

Although Shen Qi is confident in the answers to the first five questions, he doesn't know the situation of other contestants.

If you want to get a gold medal, the safest way is to answer all the questions correctly.

When Shen Qi carefully examined the last question, he felt that the person who asked this question was simply out of his mind.

The last question reads:

"Time travels to 500 BC, and you are Hippasus' younger brother, please prove that there is no ratio of an integer to an integer, and its square is 2."

"Please be careful. Your brother Hippasus was just drowned by your teacher Pythagoras. Don't try geometric construction to complete the proof, otherwise you will be drowned too."

"Once you're drowned, you don't get a single point."

Yes, this is the final question of the National Mathematics League finals, it's so dull.

It is actually very simple to convert the question surface into mathematical language, that is: please prove that the root number 2 is an irrational number.

An irrational number is an infinite non-recurring decimal, such as 1.41421356... It has no rules and is unreasonable. It just goes on endlessly and never loops.

Even junior high school students know that the root number 2 is an irrational number, and can write at least one proof method to prove that the root number 2 is an irrational number.

And Shen Qi can write at least eight methods to prove that the root number 2 is an irrational number.

This question is so simple that even second-year junior high school students can do it.

Really?

Is the truth really like this?

No, it's not.

This is the finale of the national finals, and it's not as low as you might think.

Because in the setting of the teacher who made the question, Shen Qi traveled to ancient Greece and became a student of Pythagoras and a younger brother of Hippasus.

It is impossible for a person who studies mathematics not to know the Pythagorean school and the founder of this school, Pythagoras.

Pythagoras is an ancient god in the history of mathematics. He established a mysterious organization on the island of Samos, integrating science, religion, and philosophy. In today's words, this organization is very likely to be the legendary "God of Science" teach".

The central tenet of the Pythagoreans is that mathematics is the study of abstract concepts.

Even today, in the 21st century, mathematicians also recognize the idea that Pythagoras put forward 2,500 years ago. Mathematics is the study of abstract concepts.

Pythagoras had two major hobbies in his life, studying mathematics and killing students. The smarter the students with better grades, the more he wanted to kill them.

Hippasus, a proud disciple of Pythagoras, proved that there is no ratio of an integer to an integer whose square is 2 through the method of geometric construction. This method is recorded in the textbooks of the second grade of junior high school, and it is an enlightenment chapter for junior high school students to come into contact with irrational numbers.

Then Hippasus was tied up by Pythagoras and thrown into the sea to feed the fish, let you pretend? The poser must die.

After the death of Pythagoras, the geometric proof method created by Hippasus was finally handed down to the world. The wonderful idea he bought with his life is the "square infinite tossing and dividing algorithm to find the greatest common divisor" in today's junior high school textbooks ".

In the special situation of the finale of the National Finals, Shen Qi was set by the question maker as Hippasus’ junior, so he could not use geometric methods to prove that the square root of 2 is an irrational number. Otherwise, you will be "drowned" by the question maker, and you won't even get a single point.

Among the at least eight proof methods mastered by Shen Qi, there are of course other methods, but he is Hippasus’s younger brother, and he lived 2,500 years ago. At that time, there was no prime number method, and even the root number did not appear, so Other proof methods are automatically invalid.

What is written on the title is "Please prove that there is no ratio of an integer to an integer, and its square is 2", not "Please prove that the square root of 2 is an irrational number".

So this question is perverted.

This also confirms an old saying in mathematics: simple-is-hard

The easier it is, the more difficult it is.

"Entangled, entangled, how to solve this problem under so many perverted constraints?"

Shen Qi was a little anxious, click, he used too much force and accidentally broke the pencil, his hands were covered with sweat.

In the process of solving the first five questions of the national preliminaries and national finals, Shen Qi was not without trouble.

Although he encountered troubles, Shen Qi was able to get a little bit of ideas, and followed the clues to finally get the correct answer.

As for the finale of the national final, "The Curse of Hippasus" made Shen Qi helpless, and Pythagoras' death gaze traveled through time and space made Shen Qi feel like a pain.

"What should I do, what can I do? This question is too tricky, and it has far surpassed a high school student or even a college student's understanding of mathematics. Is it possible that only graduate students or even doctoral students in the Department of Mathematics will do this? "

This is the biggest dilemma Shen Qi has encountered in the past few months. It reminds him of his time as a scumbag. I know all the words written in the title, but I don't know what to do.

Time passed by every minute and every second, and there was still half an hour left before the paper was handed in.

Shen Qi spent 2 hours on the final question and could not write a word, while he spent a total of 2 hours on the first two questions.

"Ms. Zhang, Mr. Cao, Mr. Tian, ​​you teach me how to solve this problem, which route should I take? I have no idea at all!" Students will naturally think of the teacher when they encounter difficulties, but Shen Qi found that he From elementary school to high school, all mathematics teachers have never taught a method, which can prove that the root number 2 is an irrational number without Hippasus' infinite geometry method and the algebraic method of later generations.

We all know that a person is born with one head and two arms. The difficulty is how to prove this generally accepted fact. Why not three heads and six arms? What is the real reason? Is it caused by reincarnation technology? If reincarnation technology is the real cause, please also prove it.

simple-is-hard

Shen Qi's current predicament is roughly the same, the conclusion is clear and cannot be proved.

"Ms. Zhang, Mr. Cao, Mr. Tian, ​​I may disappoint you all. I know that if I pretend too much, I will be thrown into the sea to feed the fish sooner or later. Mr. Zhang, Mr. Cao, Mr. Tian... what the fuck, Tian Teacher!" Shen Qi shuddered, a fleeting inspiration flashed through his brain like an electric shock.

"Yes, that's right, Teacher Tian, ​​the ancient Babylonian number system, sexagesimal!"

A kind of excitement of surviving after a catastrophe stirred in Shen Qi's body. Before coming to the capital, during the provincial team training, Mr. Tian had taught the sexagesimal system of the ancient Babylonian number system.

The ancient Babylonians used the ancient hexadecimal system to calculate the approximate value of the square root of 2, which was a method 5,000 years ago, and Mr. Tian's private product.

Sexagesimal is older than Pythagoras, so I'm using sexagesimal no foul! Shen Qi picked up a pen and wrote:

▲

▲▲

▲▲▲

...

◆

...

▼

...

▲▲▲-▏◆-▼

...

What Shen Qi wrote is cuneiform, and he is using cuneiform to make a proof, a pure proof of the ancient Babylonian sexagesimal number system, the oldest branch of mathematics with a history of more than 5,000 years.

In the ancient Babylonian sexagesimal number system, ▲ represents 1, ▲▲ represents 2, ▲▲▲ represents 3... The same wedge-shaped mathematical symbol can always be superimposed on 9, representing 1-9.

◆ represents 10, ▼ represents 60.

▏◆ represents the multiplication sign, and it is read as "Ai Rui" in ancient Babylonian.

▲▲▲▏◆▼ means 3 multiplied by 60, Shen Qi needs to make a sexagesimal love core, so that he can smoothly enter the special reciprocal table of the ancient Babylonian number system.

The ancient Babylonians turned the reciprocal into a sexagesimal "decimal", but they didn't realize it was a decimal at the time, so they added quotation marks.

After entering the decimal field of the ancient Babylonian reciprocal table, Shen Qi became more and more excited. His intuition told him that he was using a powerful method to prove an extremely absurd topic, and he was about to succeed!

"Hahaha, it's a divine manipulation, Tianxiu!"

Shen Qi’s proof process was all in cuneiform, and finally he wrote the answer: ▲▲◆▼▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲

At this time, the urgent bell rang, and the 4.5-hour competition time was up.

Shen Qi hastily handed in the paper and didn't have time to check it.

This is the only game he has participated in so many math competitions that he has no time to check, the national finals.

No matter what, the current national election is over, and all Shen Qi can do is to wait for the result.

At three o'clock in the afternoon, the Chinese Mathematical Society unpacked all the national final exam papers, and the marking work began.

At seven o'clock in the evening, one of the judges in the marking room was stunned. He was Director Liu of the Chinese Mathematical Society.

Officer Liu was reviewing Shen Qi's national final exam paper. When he saw that Shen Qi's last questions were all answered in cuneiform characters, he was in a bad mood: "Xiaowen, hurry up... take my quick-acting life-saving star pill... take it Come here... in my briefcase..."