How to break into a math book

These five digital passwords are indeed amazing. The numbers are so large that people have no clue.However, what bothered Tu Hua most was whether the sequence that they found in the level task was based on these five numbers themselves, or did they need these five numbers for further evolution.

如果数列的前五个数字就是【10】【1066】【8098】【66889006】【236889007589086】，这道题目的难度明显就太大了,要在这种近乎于密码译电的数字中寻找规律,实在不符合高中数学的常理。

Tu Hua turned his head and glanced at Su Gechi. This person looked like an old god, which proved that the content of this level was as he expected, and there was no danger of viruses.According to the previous difficulty of the topic, you may occasionally encounter abnormal situations, but there must be an unexpected solution to any abnormal problem.

Shen Siyi's thinking is similar to that of Tu Hua: "I think these five numbers should not be the final numbers in the sequence. The digital code... just as the name implies, it is necessary to unlock the code represented by these numbers in order to obtain the real sequence information."

Sun Wei frowned: "So... these five numbers need further analysis?"

Tu Hua nodded, stood up and said, "Well, in order to brainstorm and avoid falling into misunderstandings again, let's observe these numbers together, and then everyone will share their opinions."

Shen Siyi took the lead and said: "I think the regular relationship between these five pieces of information should not be a conventional mathematical relationship, it is very likely that it is really like a code, each number represents a different piece of information, and these five number strings are five different pieces of information. Information."

Sun Wei thought for a while, and said: "I thought these numbers had some similarities, for example, they were all even numbers, but according to what you said, it seems that I really can't get into the misunderstanding of mathematics. These numbers The four numbers 0, 6, 8, and 9 appear frequently, so I wonder if the key information lies in these four numbers?"

When it was Wang Boyu's turn, he obviously didn't think too much, and just followed Sun Wei's train of thought and added: "0689...Indeed, these numbers look very round."

Tu Huaning raised his eyebrows: "Round?"

Wang Boyu laughed and scratched his head: "That's right, judging from the shape of the Arabic numerals, these numbers are very round!"

Tu Hua froze for a moment.

Wang Boyu's words seem to have little nutrition, but they gave Tu Hua a new way of thinking.Could it be that these numbers...are not actually numbers?

In ancient times, humans invented hieroglyphs, and the meaning of characters is expressed through patterns. These numbers are likely to be just a pictographic representation. 0689 does not represent 0689, but some kind of graphics.

"Pythagoras..." Tu Hua frowned, "This level is called [Pythagoras' Beach]. So far, has anything related to Pythagoras appeared?"

Shen Siyi also thinks that Tu Hua's point is very reasonable. The name of the level must be related to the content of the level. The beach of Pythagoras only has sand, which is obviously unreasonable.This also means that there must be something related to Pythagoras in this level.

Shen Siyi tried his best to recall the life of Pythagoras: "The most famous theory of Pythagoras is the Pythagorean theorem, but if it has to be related to numbers, in the Pythagorean school, give 1 The ten numbers up to 10 have been defined. For example, 1 represents wisdom and the first principle of numbers, and 2 represents opposition and negation, which is an opinion. As for the 0689 we just discussed, Pythagorean Russ' school definitions are: nothingness, soul, emotion, and reason."

"If you look at it this way, it's a bit too mysterious." Wang Boyu couldn't believe it. "Does this coded information require us to start from a philosophical point of view? I always feel that we have gone astray."

It really can't involve philosophy.Tu Hua supported his forehead, carefully recalling the life of Pythagoras.He was a famous philosopher and mathematician in ancient Greece, and he was able to appear in this level must be because of his achievements in mathematics.

But besides the Pythagorean Theorem, what other mathematical achievements do he have... By the way, number theory!

In addition to the familiar Pythagorean theorem, Pythagoras' greatest contribution in mathematics is the unified classification and division of numbers.He connected numbers with geometry, and distinguished natural numbers into even numbers, odd numbers, square numbers, triangular numbers, and pentagonal numbers, etc.

And the Pythagorean theorem is the application of square numbers.

So does this question have anything to do with these numbers?

Tu Hua shared his ideas with his partners, but they were still unable to connect the numbers in the digital code with the special numbers classified by Pythagoras.

Tu Hua's thinking went back to the inspiration Wang Boyu gave him at the beginning.

It is definitely wrong to use these five digital codes to force Pythagorean mathematics students. Their direction at the beginning was not wrong. These five digital codes do not represent numbers. The information behind them is the same as that of Pythagoras. Russ related.

The situation seems to be back to the original point, they must find the meaning of these numbers.

"We only noticed Pythagoras, but we didn't notice the meaning of Pythagoras' beach." Sun Wei suddenly said, "The subject of the words [Pythagoras' beach] lies in 'Beach', and this beach belongs to Pythagoras, I think this is an angle that must be considered."

"I remember that Pythagoras seemed to be born near the Aegean Sea, and when he was thinking about problems... he liked to hang out on the beach." Sun Weidao, "Especially when he was studying mathematical problems, he would be like us now, Write and draw on the beach, find some pebbles to record data."

Pebbles? !

With a buzzing sound in his head, Tu Hua quickly looked at the five digital codes.

【10】【1066】【8098】【66889006】【236889007589086】……孙维说的没错，这些数字中0689这几个数字出现的频率很高，而王博宇的说法也是对的，这几个数字的形状很圆。

Pythagoras used round pebbles to record numbers when studying numbers. He would arrange the pebbles into various shapes and record the number of pebbles at the same time.

And the digital password in this question... is to use the shape method to record.

The numbers with circles in their shapes represent the pebbles that Pythagoras used to record.

In the first [10], there is only one 0 in the circle-shaped number, so the number represented by the first piece of information is 1.

In the message [1066], besides 0, there are 6 numbers in the shape of circles, so the number is the number of circles, that is, 3.

【8098】Among the four numbers, the shapes of 8 and 9 both contain circles, and 8 represents two circles, so the number of this message is 6.

依次类推，【66889006】和【236889007589086】这两串数字中，圆圈的数量分别为10和15，也就是说，这五条信息分别代表的数字是：1、3、6、10、15。

Triangle numbers!

Tu Hua suddenly realized, and all the metaphors in this level also came to light.Pythagoras once used small stones to represent points on the beach, and studied the triangular and square number sequences.

所谓三角形数列，1代表了一个点，3代表用三个点可以组成一个三角形，6代表用六个点也可以组成一个三角形。三角形数是数列中最基础的一种，如果用数列的规律表达，第n个数字就是n（n1）/2，按照目前的1、3、6、10、15的数字规律来看，3比1大了2，6比3大了3，10比6大了4，15比10大了5。

According to this increasing law, the number following 15 should be 21.

Tu Hua quickly expressed his thoughts and analysis. Although the idea of ​​using a number-shaped circle to represent a point is very wild and unconstrained, it has to be said that this is the most irrefutable answer.

涂化按照规则的要求在沙滩上写下了这个数列的前十个数字，就像当初的毕达哥拉斯一样，把思维和智慧留在沙滩上：1、3、6、10、15、21、28、36、45、55。

After Tu Hua finished writing, he looked back at Su Gechi, and found that he was standing where the sand meets the waves, looking at this side with a calm expression.The afterglow of the setting sun painted a layer on his body, and Tu Hua suddenly felt that Su Gechi was like Pythagoras who led him into mathematics.

He used to hate mathematics, thinking that mathematics was just a lifeless subject, but it was not until he met Su Gechi that he discovered that mathematics had so many rich and wonderful connotations.

Mathematics is a subject that has fascinated a series of philosophers such as Pythagoras and Hipparchus. It is all-encompassing, sometimes rigid and rational, and sometimes lively and lovely. It is not what Tu Hua used to understand.In the game of Mathematics Breakthrough, he experienced the joy of immersing himself in mathematics for the first time, and he felt the resonance between his jumping thinking and mathematics.

Even if there is a virus in the game, even if his original intention of breaking through the level is quite different from Su Gechi's previous setting, he still enjoys the feeling of wandering freely in mathematics.

Mathematics is not only the combination and transformation of numbers, but also the collision and attraction of souls.

【Ding--】

[Congratulations to the challengers Tu Hua, Shen Siyi, Wang Boyu, and Sun Wei for clearing the Pythagoras beach level. Sun Wei got the representative number 9. 】

It was only then that Tu Hua remembered the main task of [Sequential Level].

Within 48 hours, each of them must obtain their own number. Now only Sun Wei has obtained the number 9 among the four, and a third of the time has passed. The other three are on the verge of danger. Speed ​​up the customs clearance to get the number imminent.