I just want to be a quiet scholar

Chapter 35 Yes, there is such an operation

"Last question, one last question left."

Although Shen Qi had confidence in the answers to the first five questions, he did not know the status of the other players.

If you want to get the 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 insane.

The last question is written like this:

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

"Please be careful, your brother Hippasus has just been drowned by your teacher Pythagoras. Don't try geometric construction to complete the proof, otherwise you will also drown."

"Once you drown, you won't get a single point."

Yes, this is the finale of the National Mathematics League Finals, it's so dull.

It is actually very simple to convert the title into mathematical language, namely: please prove that the square root of 2 is an irrational number.

An irrational number is an infinite and non-repeating decimal, such as 1.41421356... It has no rules and is unreasonable, and it extends endlessly without looping.

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

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

This question is so simple that every second year student can do it.

really?
Is the truth really like this?
No, it's not.

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

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

It is impossible for anyone who studies mathematics not to know about the Pythagoreans, 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 most likely the legendary "God of Science". teach".

The core tenet of the Pythagoreans is the mathematical study of abstract concepts.

Even today in the 21st century, mathematicians have also acknowledged the view put forward by Pythagoras 2500 years ago that mathematics deals with abstract concepts.

Pythagoras had two hobbies in his life, studying mathematics, and killing students. The smarter the student, the better the score.

Hippasus, a proud disciple of Pythagoras, proved through geometric construction that there is no ratio of integers to integers whose square is 2.This method is recorded in the textbook of the second grade of junior high school, which is the enlightenment chapter for junior high school students to contact irrational numbers.

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

After the death of Pythagoras, the geometric proof method created by Hippasus finally spread to the world. ".

In the special context of the final question of the national final, Shen Qi was set by the questioner as the junior and junior of Hippasus, so he could not use the geometric method to prove that the square root of 2 is an irrational number.Otherwise, you will be "drowned" by the questioner, and you won't even get a point.

Among the at least eight proof methods that Shen Qi has mastered, there are of course other methods, but he is the junior and junior brother of Hippasus, who lived 2500 years ago. At that time, there was no prime number method, and even the root sign did not appear, so Other proof methods are automatically invalid.

The title says "Please prove that there is no ratio of an integer to an integer whose 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.

"Tangled, tangled, with so many perverted constraints, how to solve this problem?"

Shen Qixian was a little anxious, click, he used too much force and accidentally broke the pencil, his palms were full of sweat.

In the process of solving the first five questions of the National Preliminary and National Final, Shen Qi was not without trouble.

Although he was in trouble, Shen Qi could always get a little idea and follow the vine to get the correct answer.

As for the finale of the national final, "The Curse of Hippasus" left Shen Qi helpless, and the death gaze of Pythagoras crossed time and space, leaving Shen Qi on his back.

"What should I do, what can I do? This question is too tricky, far beyond a high school student or even a college student's understanding of mathematics. Maybe only a graduate student or even a doctoral student in the Department of Mathematics can do it? "

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

Minutes and seconds passed, and there was still half an hour left before the paper was handed over.

Shen Qi spent 2 hours on the final question and couldn't write a single word, and he spent 2 hours in total on the first two questions.

"Mr. Zhang, Mr. Cao, Mr. Tian, ​​you teach me how to solve this problem, and what kind of route should I take? I have no ideas at all!" When students encounter problems, they will naturally think of the teacher, but Shen Qi found that he From elementary school to high school, all math teachers have never taught a method to prove that the square root of 2 is irrational without using the Hippasus infinite geometry method and the algebraic method of later generations.

We all know that people are 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 the reincarnation technique? If the reincarnation technique is the real cause, please prove it.

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

"Teacher Zhang, Teacher Cao, Teacher Tian, ​​I may have to disappoint you. I know that if I pretend to be too much, sooner or later, I will be thrown into the sea to feed the fish. Teacher Zhang, Teacher Cao, Teacher Tian...Fuck, Tian Teacher!" Shen Qi was stunned, and a fleeting inspiration rushed through his brain like an electric shock.

"Yes, that's right, Mr. Tian, ​​the Babylonian number system, sexagesimal!"

A thrill of the rest of his life stirred in Shen Qi's body. Before coming to the capital, when the provincial team was training, Teacher Tian taught the sexagesimal system of the Babylonian number system.

The ancient Babylonians used the ancient sexagesimal system to calculate the approximate value of the square root of 2, which was a method 5000 years ago, and Mr. Tian's private goods.

Sexagesimal is older than Pythagoras, so I am not fouled using sexagesimal!Shen Qi picked up the pen and wrote:

▲

▲▲
▲oqueroquer

……

◆

……

▼

……

▲▲▲-▏◆-▼

……

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 5000 years.

In the Babylonian sexage system, ▲ stands for 1, ▲▲ stands for 2, ▲▲▲ stands for 3... The same cuneiform mathematical notation can always be superimposed on 9, representing 1-9.

◆ represents 10, ▼ represents 60.

▏◆ represents the multiplication sign, which is pronounced "Airi" in the Babylonian language.

▲▲▲▏◆▼ means 3 times 60, Shen Qi needs to be a sexagenary Ai Rui, so that he can smoothly enter the special reciprocal table of the Babylonian number system.

The ancient Babylonians converted the reciprocal to sexagesimal "decimal", but they didn't realize it was a decimal at the time, so they put it in 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 proving an extremely absurd problem with an awesome method, and he was about to succeed!

"Hahaha, it's just a god operation, Tianxiu!"

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

At this time, the tight bell rang, and the 4.5-hour competition time had come.

Shen Qi hurriedly handed in the papers and didn't have time to check.

This is the only game he has played in so many numbers competitions that he has no time to check, the national final.

No matter what, this national final is over, all Shen Qi can do is wait for the result.

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

At seven o'clock in the evening, a grading judge in the grading room was dumbfounded. He was Director Liu of the Chinese Mathematical Society.

Secretary Liu was grading Shen Qi's national final exam paper, and when he saw that Shen Qi's last question was all answered in cuneiform, his whole person was in a bad mood: "Xiao Wen, hurry... hurry up and take my quick-acting savior... Come here...in my briefcase..."

(End of this chapter)