"The last question, the last question left. ”

Although Shen Qi was confident in the answers to the first five questions, he didn't know the situation of the other players.

If you want to win a gold medal, the safest thing to do is to answer all the questions correctly.

When Shen Qi carefully examined the last question, he felt that the person who came up with this question was simply a dull soul.

The last question reads:

"Time traveled to 500 B.C., and you are the brother of Hippassus, please prove that there is no such thing as an integer to an integer ratio, which is squared by 2. ”

"Please be careful, your brother Hipassus has just drowned in Pythagoras, and do not attempt geometric drawing to complete the proof, or you will be drowned. ”

"Once you're drowned, you won't get even a point. ”

Yes, this is the finale of the National Mathematics League finals, and it's so bleak.

The translation of the problem into mathematical language is actually very simple, i.e., please prove that the root number 2 is an irrational number.

An irrational number is an infinite non-cyclic decimals, such as 1.41421356...... It has no rules, it doesn't make sense, it just goes on endlessly, and it never goes on in 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.

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

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

Are you sure?

Is this really the case?

No, not really.

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

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

It is impossible for a student of mathematics not to know about the Pythagoreans and the founder of this school, Pythagoras.

Pythagoras, the ancient god of mathematics, founded a mystical organization on the island of Samos, combining science, religion, and philosophy, which is most likely the legendary "Church of Scientology" in today's terms.

The core tenet of the Pythagoreans was the study of abstract concepts in mathematics.

To this day in the 21st century, mathematicians have acknowledged the idea that Pythagoras made 2,500 years ago that mathematics is the study of abstract concepts.

Pythagoras had two great passions in his life, studying mathematics, and killing students, and the smarter the students, the better the students, the more they wanted to kill.

Hippassus, a proud disciple of Pythagoras, proved by geometric drawing that there is no such thing as a ratio of an integer to an integer number, which is squared to 2. This method is recorded in the textbook of the second grade of junior high school, and it is the beginning of junior high school students' exposure to irrational numbers.

Then Hypatsus was tied up by Pythagoras and thrown into the sea to feed the fish, and you must die.

After the death of Pythagoras, Hippasus's geometric proof method was finally popularized in the world, and the whimsy he exchanged his life for 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 decision, Shen Qi was set by the questioner to be the junior brother of Hippassus, so he could not use the geometric method to prove that the root number 2 was an irrational number. Otherwise, you will be "drowned" by the questioner, and you won't even get a point.

Of the at least eight proof methods that Shen Qi mastered, of course, there were other methods, but he was the younger brother of Hippassus, and lived 2,500 years ago, when the prime number method did not exist, and even the root number did not appear, so the other proof methods automatically failed.

The inscription reads, "Please prove that there is no ratio of an integer to an integer and that its square is 2", not "Please prove that the root number 2 is irrational".

So this question is very perverted.

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

The simpler it is, the more difficult it is.

"Tangled, tangled, under the restrictions of so many perverts, how to solve this problem?"

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

In the process of solving the first five questions of the national pre-announcement and the national decision, Shen Qi did not encounter trouble.

Although he encountered trouble, Shen Qi was able to get a little bit of thought, and finally got the correct answer.

And the finale of the national decision, "The Curse of Hippassus" made Shen Qi helpless, and Pythagoras's death gaze traveled through time and space to make Shen Qi like a man.

"What should I do, what can I do? This question is so tricky that it far exceeds the knowledge of a high school student or even a college student, and this may only be done by a graduate student or even a doctoral student in the Department of Mathematics, right?"

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

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

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

"Teacher Zhang, Teacher Cao, Teacher Tian, you teach me how to solve this problem, what kind of route to take? I have no idea at all!" Students naturally think of the teacher when they encounter a problem, but Shen Qi found that from elementary school to high school, all the math teachers have never taught a method to prove that the root number 2 is an irrational number without the Hippassus infinite geometry method and the algebraic method of later generations.

We all know that people are born with one head and two arms, but the difficulty is how to prove this accepted fact, why not three heads and six arms, what is the real reason? Is it caused by reincarnation technology, and if reincarnation technology is the real cause, please also prove it.

simple-is-hard

Shen Qi's current predicament is roughly like this, the conclusion is clear, and it cannot be proven.

"Teacher Zhang, Teacher Cao, Teacher Tian, I may be about to disappoint you, I know that if you pretend to be too much, sooner or later you will be thrown into the sea to feed the fish. Teacher Zhang, Teacher Cao, Teacher Tian...... , Mr. Tian!" Shen Qi was excited, and a fleeting inspiration was like an overpower in his brain.

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

A kind of stimulus for the rest of his life after the catastrophe stirred in Shen Qi's body, before coming to the capital, when he was training in the provincial team, Mr. Tian taught the hexadecimal system of the ancient Babylonian number system.

The ancient Babylonians used the ancient sexagesimal system to calculate the approximation of the root number 2, which was the method 5,000 years ago, and Mr. Tian was the private goods.

The sexagesimal system is older than Pythagoras, so I don't foul it when I use the hexagesim system!

▲

▲▲

▲▲▲

......

◆

......

▼

......

▲▲▲-▏◆-▼

......

Shen Qi wrote cuneiform, and he was using cuneiform to prove that the pure ancient Babylonian sexagesimal number system proved that it was the oldest branch of mathematics in the history of more than 5,000 years.

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

◆ 10 for 1, ▼ for 60.

▏◆ represents the multiplication sign, which is pronounced "Airui" in ancient Babylonian.

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

The ancient Babylonians turned the reciprocal to a "decimal number" in the hexagesimal system, but they didn't realize it was a decimal at the time, so they put quotation marks.

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

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

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

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

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

It was the only one he had competed in, the only one he didn't have time to check, the national final.

In any case, this national decision is over, and all Shen Qi can do is wait for the result.

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

At seven o'clock in the evening, a marking judge in the marking room was dumbfounded, he was Secretary Liu of the Chinese Mathematical Society.

Officer Liu was reviewing Shen Qi's national final examination papers, and when he saw that Shen Qi's last question was all answered in cuneiform, the whole person was not good: "Xiaowen, hurry up...... Hurry up and take my quick-acting savior pills...... Bring it over...... ...... in my briefcase"