I Just Want to Be a Quiet Top Student

　　 "The last question, there is the last question left."

　　 Although Shen Qi is confident in the answers to the first five questions, he does not know the status of other players.

　　 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 came up with it was simply faint.

　　The last question is written like this:

　　 "Time travels to 500 BC, and you are Hipassus's 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 Hipassus has just been drowned by your teacher Pythagoras. Don't try geometric construction to complete the proof, otherwise you will also be drowned."

　　 "Once you are drowned, you won't get even one point."

　　 Yes, this is the finale of the National Mathematical League Finals.

　　 The conversion of the question surface into mathematical language is actually very simple, that is, please prove that the root number 2 is an irrational number.

　　 Irrational numbers are infinite non-recurring decimals, such as 1.41421356...It is irregular, unreasonable, and just extends endlessly, never looping.

　　 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, it will be done by the second grade students.

really?

Is the truth really like this?

　　 No, it is not.

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

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

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

Pythagoras is an ancient **** in the history of mathematics. He established a mysterious organization on the island of Samos, integrating science, religion, and philosophy. In current terms, this organization is most likely the legendary "Science God". teach".

　　 The core purpose of the Pythagorean School is: mathematical research on abstract concepts.

　　 Until today in the 21st century, mathematicians also admitted that Pythagoras made the point 2500 years ago that mathematics studies abstract concepts.

　　 Pythagoras has two major hobbies in his life, studying mathematics, and killing students. The smarter the student, the better the student will kill.

　　Hipassus was a proud disciple of Pythagoras. He proved that there is no ratio of an integer to an integer, and its square is 2. This method is recorded in the textbook of the second grade of junior high school, and it is the enlightenment chapter for junior high school students to get in touch with irrational numbers.

　　 Then Hipassus was **** by Pythagoras and thrown into the sea to feed the fish, let you pretend? The pretender must die.

After the death of Pythagoras, the geometric proof method created by Hipassus was finally passed on to the world. The ingenuity he exchanged for his life is the "square infinite divide algorithm found in the junior high school textbook today to find the greatest common divisor." ".

　　In the special context of the finale of the National Judgment Question, Shen Qi was set by the person who made the question as the junior of Hipassus, so he could not use the geometric method to prove that the root number 2 is an irrational number. Otherwise, you will be "drowned" by the questioner and won't even get a point.

Of the at least eight methods of proof that Shen Qi has mastered, of course there are other methods, but he is Hipassus’s younger brother, who lived 2500 years ago, there was no prime number method in that era, and even the root sign did not appear, so Other proof methods are automatically invalidated.

　　 says "Please prove that there is no ratio of an integer to an integer, and its square is 2" instead of "please prove that the root number 2 is an irrational number".

　　 So this question is very perverted.

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

　　 The simpler, the more difficult.

　　 "Entangled, entangled, under so many perverted restrictions, how can this problem be solved?"

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

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

　　Although he is in trouble, Shen Qi can always get a little idea, and finally get the correct answer.

　　 And the country’s finale, "The Curse of Hipassus" made Shen Qi helpless, and Pythagoras’s death gaze across time and space left Shen Qi on his back.

"What should I do, what can I do? This question is so tricky that it far exceeds the knowledge of mathematics by a high school student or even a college student. Isn't it possible that only graduate students or even doctoral students in the Department of Mathematics can do it? "

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

　　 Time passed by one minute and one second, and half an hour was left before the papers were handed in.

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

"Teacher Zhang, Teacher Cao, Teacher Tian, ​​do you teach me how to solve this problem, and which route to follow? I have no idea 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, none of the mathematics teachers taught a method to prove that the root number 2 is an irrational number without using the Hipasus infinite geometry method and later algebraic methods.

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

　　Simple-is-hard

　　 The predicament that Shen Qi is facing now is roughly the same, with a clear conclusion that cannot be proved.

"Teacher Zhang, Teacher Cao, Teacher Tian, ​​I may disappoint you. I know that I will pretend to be too much, and one day I will be thrown into the sea to feed fish. Teacher Zhang, Teacher Cao, Teacher Tian... Fuck, Tian Teacher!" Shen Qi was agitated, and a fleeting inspiration fluttered in his brain like an electric shock.

　　 "Yes, that's right, Mr. Tian, ​​Babylonian number system, six decimal system!"

　　 A kind of surviving stimulus stirred in Shen Qi's body. Before coming to the capital, during the training of the provincial team, Mr. Tian taught the Babylonian number system six decimal system.

　　 The ancient Babylonians used the ancient six-decimal system to calculate the approximate value of the root number 2. This is the method 5000 years ago, and Mr. Tian’s private goods.

　　 The six-decimal system is older than Pythagoras, so I use the six-decimal system to not violate the rules! Shen Qi wrote:

　　▲

　　▲▲

　　▲▲▲

　　……

　　◆

　　……

　　▼

　　……

　　▲▲▲-▏◆-▼

　　……

　　 Shen Qi writes cuneiform writing. He is using cuneiform writing to prove, the pure Babylonian six-decimal number system, the oldest branch of mathematics in the history of more than 5,000 years.

　　 In the Babylonian six-decimal number system ~www.readwn.com~ represents 1, ▲▲ represents 2, ▲▲▲ represents 3... The same wedge-shaped mathematical notation can always be superimposed with 9, representing 1-9.

　　◆ stands for 10 and ▼ stands for 60.

　　▏◆ stands for multiplication sign and is pronounced "Airui" in Babylonian.

　　▲▲▲▏◆▼ means that 3 is multiplied by 60. Shen Qi needs to make a six-decimal erui so that he can enter the special countdown table of the Babylonian number system smoothly.

　　 The Babylonians turned the reciprocal into a six-decimal "decimal number". In fact, they didn't realize that it was a decimal number, so they added quotation marks.

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

　　 "Hahaha, it's a **** operation, Tianxiu!"

　　 Shen Qi used cuneiform writing in all his proof process, and he finally wrote the answer: ▲▲◆▼▲▲▲▲▲▲▲▲……

　　 At this time, a tight bell rang, and 4.5 hours of competition time has come.

　　 Shen Qi hurriedly handed in the papers and did not have time to check.

　　 This is the only one where he has participated in so many math competitions and there is no time to check, the national final.

　　 No matter what, the current national finals is over, what 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 scoring work began.

　　 At seven o'clock in the evening, a scoring judge in the scoring room was dumbfounded. He was Officer 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 question was answered in cuneiform, the whole person was not good: "Small news, hurry...get my quick-acting savior pill... Come here... in my briefcase..."