After everyone else left, Ge Juntian smiled and said to Jiang Shuiyuan and Zhang Jin: "Okay now, the idle people have dispersed, and the classroom has finally quieted down, so we can talk about math problems! But before we talk about math problems, I must ask you a question: Are you interested in learning math? In other words, do you think math is beautiful?"

Zhang Jin's eyes emitted a strange brilliance, and he stammered: "Mathematics and mathematics are very beautiful, I have and am interested!"

Ge Juntian looked at Jiang Shuiyuan with hope again, but Jiang Shuiyuan gave him a slap in the face: "I don't think mathematics is beautiful, and my interest is mediocre!"

"Then why did you participate in the selection of the Olympiad Society? just to add points to the college entrance examination?" Ge Juntian leaned forward slightly, and his tone was a little urgent.

"It's not entirely for the college entrance examination," Jiang Shuiyuan replied calmly, "I participated in the selection of the Olympiad Club, on the one hand, it is very important to hear people say that the questions are difficult, and I can deepen my understanding of knowledge, so I want to see what I can do."

"This is interest! This is the unremitting inquiry into knowledge, without any utilitarian tendencies! Many geniuses start by testing their own abilities and gradually transition to academic research!" Ge Juntian immediately made such a judgment, "As for how beautiful you don't think mathematics is, it's not to blame you, but because you haven't met a competent teacher to show you the mysteries of mathematics." Mathematics has great beauty, it encompasses all things in the world, and it contains the supreme principles of heaven; it can be a simple and practical concrete problem in life, or an abstract theory in books, and it can also be a good tool for solving problems in work! As long as people live in society, they have to deal with mathematics almost all the time. ”

Jiang Shuiyuan was completely noncommittal to what Ge Juntian said, and just spit out two words lightly: "Hehe." ”

Ge Juntian instantly felt a lot of pressure.

The world only knows that it is difficult to find good teachers, but they do not know that it is even more difficult to find good students who suit the teacher's wishes! Because good teachers are often famous, even if Zhuge Liang lived in seclusion in a mountain village, there were Sima Hui, Xu Shu and others who knew his talent and praised him everywhere, and as long as they spent some energy, financial and material resources, they could always find it. But how can a teacher pick out his or her protégés from a large number of students who are not well-known or talented? It is generally believed that students with good grades and good performance are more likely to become talents, but in fact the situation is often the opposite. Therefore, it takes both discerning and luck to select students. And once found, it can easily be recorded in history with the tail attached. In history, many people with mediocre talents have gone down in history because he discovered and cultivated one or several famous disciples. If it weren't for Abel, a mathematical genius, who would have remembered that there was a teacher in Norway named Holmbo?

And if Ge Juntian wants to realize his dream of being a gold medal coach in the Olympiad, he needs a talented student even more.

Seeing that thousands of choices finally found a favorite candidate, who knew that this duck in hand was impatient to obey his own discipline, and wanted to flap his wings and fly away all the time. But how could he let him fly away from his hands? So Ge Juntian decided to make some drastic predictions: "Maybe you think that there are such mathematical problems in life? How can mathematics have a beautiful existence? Then I'll give you an example! For example, when you wash clothes at home every day, soak and rub the clothes first, and then twist them." Of course, you can't wring the water out completely, and you have to rinse it with clean water before drying. Assuming that there is still 1 kg of dirty water remaining on the clothes, rinse with 20 catties of clean water, how can you rinse the clothes to the cleanest?

"Most people put all their clothes in 20 catties of water at once and rinse them. Then together with the original 1 catty of water on the clothes, there are now a total of 21 catties of water. Assuming that the dirt is evenly distributed in the 21 catties of water, after wringing out, there is still 1 catty of water left on the clothes. So if you dry it directly after washing, how much dirt remains as much as it was?"

"One in twenty-one!" Zhang Jin didn't stutter when he answered this question.

"Very good!" Ge Juntian nodded, "Of course, there will be some diligent people who will use these 20 catties of water to rinse the clothes twice." For example, wash it once with 5 catties of water, and then wash it again with the remaining 15 catties of water. How much filth is there?"

Zhang Jin picked up the pen and was about to calculate, but Jiang Shuiyuan replied a little impatiently: "One ninety-six!"

The amount of dirt residue on the clothes has been greatly reduced, which fully shows that diligent people are still very rewarded. Although Ge Juntian knew that Jiang Shuiyuan's mental arithmetic ability was very strong, when he heard him report the correct answer at this time, his eyes were still full of brilliance: "But if you wash the clothes twice, the choice of each family is different, some use 4 catties for the first time, 16 catties for the second time, and some use 7 catties first, and then 13 catties." Now the question arises, how to distribute the water reasonably to minimize the amount of dirt residue on the clothes in two rinses?"

"10 catties, 10 catties!" "It's 10 catties every time!" Zhang Jin and Jiang Shuiyuan almost reported the correct answer in unison.

"It seems that both of you are very good at math!" said Ge Juntian with satisfaction, "Yes, in this way, the amount of dirt residue will be reduced to 1/121." In this way, it is inevitable that some people will think that if you rinse it four times with five catties of water each time, the effect is better? The answer is obviously yes, but ordinary people will never use this washing method, it is too troublesome. But mathematicians will tirelessly ask: Is it true that the more evenly the water is washed, the better the rinse will be, is it the more often washed, the cleaner it is, and what is the cleanest?"

Without much thought, the answer to the first two questions must be "yes", and the key is how to prove it. As for the last question, you need to think about it!

Just as the two of them were thinking, Ge Juntian got up and took out a few books from the belly of the podium and handed them to Jiang Shuiyuan and Zhang Jin: "You might as well go back and think about this issue carefully and give detailed proof." As long as you can do it, or feel that you can't do it, you can always come to the sophomore mathematics department to find me. In addition, I have a few interesting books here, one is the "Biography of the World-Famous Mathematician" organized by the Institute of Mathematics of the Chinese Academy of Sciences, the other is the autobiography of the American mathematician Halmos "I want to be a mathematician", the other is the "Collection of Mathematical Interesting Facts" by the American female journalist Papas, and several "Mathematics and the Story of Mathematicians", you can read it when you have time, you can find that mathematics is definitely a beautiful and interesting thing!"

For reading, Jiang Shuiyuan is not excluded, especially this kind of popular science books that increase knowledge and broaden horizons. He and Zhang Jin agreed to take a few copies each, and exchange them with each other after reading them. Because of this, Jiang Shuiyuan learned that Zhang Jin and Han Yun were in the same class, and the two instantly found a common topic outside of mathematics.

Jiang Shuiyuan returned to the classroom to continue his evening self-study, originally planning to continue to preview the sophomore course, but he was unsure of the question assigned by Ge Juntian, so he had to take out a pen and paper and start to find out, which took him half an hour, and took advantage of the "mean inequality" of the sophomore course he had just previewed , finally proved the first two problems, and came to the conclusion: if you rinse with 20 catties of water, and there is still 1 catty of water left after the clothes are wrung out, then no matter how you wash it, the dirt will not be less than one of the original 2 to the 40th power!

After finishing the question, he still felt unfinished, and began to look through the "Biography of the World-Famous Mathematician" that Ge Juntian lent him. It doesn't matter if you look at it, the more you look at it, the more terrified Jiang Shui Yuan will be. After class, he didn't care about talking nonsense with Wu Zichen, so he immediately went to class 11 to call out Zhang Jin, and first handed him the answer to that question: "This is the answer to the question assigned by Teacher Ge just now, please help me hand it over to him!"

"You, you've made it, I just thought about a lesson, but I didn't prove it!" Speaking of this, Zhang Jin's face was a little gloomy, after all, not everyone is willing to be subservient, especially when he was a high-minded teenager. Then he asked again, "Then why don't you just give the answer to Teacher Ge?"

"It's normal that you can't prove it now, because it uses the knowledge point 'mean inequality' in the first semester of the second semester of high school, that is, the harmonic mean does not exceed the geometric mean, the geometric mean does not exceed the arithmetic mean, and the arithmetic mean does not exceed the square mean. When you learn this knowledge point, it will be much easier to prove!" Jiang Shuiyuan first comforted Zhang Jin, and then answered his question: "The reason why I didn't directly hand over the answer to Teacher Ge is because I won't participate in the math group activities in the future!"

"Why?" Zhang Jin was shocked.

Whether it is from Ge Juntian's recognition of Cheng Dù or his own natural IQ, there is no doubt that Jiang Shuiyuan is the No.1 in mathematics of the Olympiad Society, but he did not expect him to choose to give up in a blink of an eye. How did this not surprise Zhang Jin?

Jiang Shuiyuan shook his head and said: "Because when I was reading the "Biography of World-Famous Mathematicians", I found that many mathematicians were very short-lived, especially the ones mentioned by Teacher Ge in class, such as the genius mathematician Ramanujan in Tianzhu only lived to be 33 years old, the famous mathematician Abel of Wandao only lived to be 27 years old, and the Gallic genius mathematician Galois only lived to be 21 years old, in addition to the Rakshasa mathematician Kovalevskaya, the Hanse mathematicians Riemann and Hankel, and the Gallic mathematician Pascal...... For the sake of my own life, I decided to stay away from math!"

Zhang Jin obviously thought that what Jiang Shuiyuan said was a clumsy excuse, so he raised the answer paper in his hand: "Then you still hand in your homework?"

Jiang Shuiyuan replied: "I handed in my homework to prove that I could stay in the math group, and then I quit the club to prove that I didn't want to stay in the math group." The two are not contradictory!"