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

Although Shen Qi was confident in answering the first five questions, he did not 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 indifferent.

The last question is written like this:

"Time traveled to 500 BC, and you are Hipasus' junior brother. Please prove that there is no ratio of an integer to an integer, its square is 2."

"Please be careful, your senior brother Hipasus has just been drowned by your teacher Pythagoras. Never try geometric drawing to complete the proof, otherwise you will also be drowned."

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

Yes, this is the finale of the National Mathematics League final, and it’s so indifferent.

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

Irrational numbers are infinite and non-circulating decimals, such as 1.41421356... It has no rules and is unreasonable, and it just extends endlessly, and never cycles.

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

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

This question is so simple, and students in the second grade of junior high school can do it.

Really?

Is this really the case?

No, not.

This is the finale of the National Finals, not as low as you think.

Because in the setting of the question-setting teacher, Shen Qi traveled to ancient Greece and became a student of Pythagoras and Hipasus' junior brother.

It is impossible for those who study mathematics to know about the Pythagoras, and the founder of this school, Pythagoras.

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

The core purpose of Pythagorasism is to study abstract concepts in mathematics.

Until today in the 21st century, mathematicians also acknowledged the view proposed by Pythagoras 2,500 years ago that mathematics studies abstract concepts.

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

Hipassus is a proud disciple of Pythagoras. Through geometric drawing, he proved that there is no ratio between an integer and an integer, and its square is 2. This method is recorded in the second grade of junior high school textbook and is an enlightenment chapter for junior high school students to come into contact with irrational numbers.

Then Hipassus was tied up by Pythagoras and threw it into the sea to feed fish. Let you show off? The pretender must die.

After Pythagoras's death, the geometric proof method created by Hipasus was finally passed down to the world. The wonderful ideas he exchanged for his life are the "infinite square division algorithm to find the greatest common divisor" in today's junior high school textbooks.

In the special question of the finale of the National Final Question, Shen Qi was set by the questioner as Hipassus' junior brother, so he could not use geometry to prove that the root number 2 is an irrational number. Otherwise, he would be "drowned" by the questioner and would not even get a single point.

Of course, there are other methods among the at least eight proof methods mastered by Shen Qi, but he was Hipasus' junior brother. He lived 2,500 years ago. In that era, there was no prime number method, and even the root number did not appear, so other proof methods automatically failed.

The title says "Please prove that there is no ratio of an integer to an integer, 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 the mathematics community: simple-is-hard

The simpler it is, the more difficult it is.

"I'm confused, I'm confused. Under so many perverted restrictions, how should I solve this problem?"

Shen Qi looked a little anxious. He tried too hard and accidentally broke the pencil, his palms were covered in sweat.

Shen Qi was not without trouble in solving the problems of the national preparatory and the first five questions of the national finals.

Although he encountered trouble, Shen Qi could get a little idea and follow the clues to finally get the correct answer.

The finale of the National Decision, "The Curse of Hipsus" made Shen Qi helpless, and Pythagoras's death stare traveled through time and space, made Shen Qi feel like a ray of light on his back.

"What should I do, what can I do? This question is too tricky, far exceeding the understanding of mathematics by a high school student or even a college student. Maybe only graduate students or even doctoral students in the mathematics department can do it, right?"

This was the biggest dilemma that Shen Qi had encountered in the past few months. This reminded him of his poor study period. I knew all the words written on the topic, but I just didn't know how to do it.

Time passed minute by minute, and half an hour was left before the paper was handed over.

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

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

We all know that when a person is born, he has one head and two arms. The difficulty is how to prove this recognized fact. Why is it 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 prove it.

simple-is-hard

The dilemma that Shen Qi is facing now is roughly like this, and the conclusion is clear and cannot be proved.

"Teacher Zhang, Teacher Cao, Teacher Tian, ​​I may disappoint you. I know that if you pretend too much, you will be thrown into the sea to feed fish one day. Teacher Zhang, Teacher Cao, Teacher Tian... Damn, Teacher Tian!" Shen Qi was shocked, and a fleeting inspiration moved in his brain like electricity.

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

A stimulus of the survivor after the disaster stirred up in Shen Qi's body. Before coming to the capital, when he was training in the provincial team, Teacher Tian taught the six-decimal system of the ancient Babylonian number system.

The ancient Babylonians used the ancient hexadecimal system to calculate the approximate value of root number 2. This was a method 5,000 years ago, Mr. Tian’s private goods.

The hectares are older than Pythagoras, so I use the hectares without foul! Shen Qi wrote:

▲

▲▲

▲▲▲

...

?

...

▼

...

?▼

...

▲▲▲-?◆-▼

...

Shen Qi wrote cuneiform characters, and he used cuneiform characters to make proofs, pure proofs of the hectares of ancient Babylonian hectares, and the oldest branch in the history of more than 5,000 years.

In the ancient Babylonian hectares system, ▲ represents 1, ▲▲ represents 2, ▲▲▲ represents 3... The same wedge-shaped mathematical notation can be superimposed all the time, indicating 1-9.

?Represents 10, ▼Represents 60.

?◆Represents multiplication sign, and is read as "Airui" in ancient Babylonian language.

▲▲▲-?◆-▼ means that 3 is multiplied by 60. Shen Qi needs to make a six-decimal Airui, so that he can successfully enter the special countdown table of ancient Babylonian numbers.

The ancient Babylonians converted the countdown to a "decimal" in hexadecimal. In fact, they did not realize that it was a decimal at that time, so they added quotes.

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

"Hahaha, it's simply a magical operation, Tianxiu!"

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

At this time, the rushing ringtone rang, and the 4.5-hour competition time had arrived.

Shen Qi hastily handed over the paper and had no time to check it.

This is the only competition he has participated in so many counting competitions, and has no time to check, the national final.

No matter what, this national finals have ended, and all Shen Qi can do is wait for the results.

At three o'clock in the afternoon, the Chinese Mathematics Association unpacked all national finals and the marking work began.

At seven o'clock in the evening, a judge in the marking room was stunned. He was Secretary Liu from the Chinese Mathematics Society.

Secretary Liu was reviewing Shen Qi's national finals. When he saw that Shen Qi's last question was answered in cuneiform, he was completely dissatisfied: "Xiaowen, hurry up... take my quick-acting savior pills... and put it in my briefcase..."
Chapter completed!