Volume 1: Student Life Chapter 175 The End of the Performance
Zhang Zhongyuan had a subtle look on his face. He waved his hand, motioning Chen Zhou to sit down.
This time, he is stealing my words again...
After Chen Zhou sat down, he looked at Zhang Zhongyuan with interest.
He didn't think that if it was really as others said, Zhang Zhongyuan would have nothing to say.
As expected.
Zhang Zhongyuan coughed lightly and said, "Student Chen Zhou has explained to us in detail the significance of the series verification method and also gave examples to illustrate its flaws."
"But just because it has flaws doesn't mean it has no research value."
Zhang Zhongyuan's words immediately attracted the attention of all the students to himself again.
Seeing this, Zhang Zhongyuan smiled slightly, turned around and wrote a few words on the whiteboard [Ignore even numbers and do not record them].
But for some reason, when he wrote these words, he suddenly thought of the topic discussion when Chen Zhou first participated in the project.
Suppressing this inexplicable thought, Zhang Zhongyuan turned around and glanced at Chen Zhou before continuing, "The example Chen Zhou gave just now is a general formula for even numbers. What if we ignore even numbers and only use the verification method for odd numbers?"
After hearing Zhang Zhongyuan's words, all the students except Chen Zhou fell into deep thought.
Zhao Qiqi, who was beside Chen Zhou, even tilted his head and asked Li Li, "If we just verify the odd number, it seems to work, right?"
Li Li didn't say anything, but just glanced at Chen Zhou over Zhao Qiqi.
Chen Zhou naturally knew this new verification method, but it also had its flaws.
Chen Zhou has been looking at Zhang Zhongyuan. He hopes to see Zhang Zhongyuan come up with a different idea.
Zhang Zhongyuan picked up the soaked wolfberries on the table, took a sip, and glanced at the time.
The time was just enough for him to finish this part and to encourage his classmates to think.
After covering the cup and placing the blanket on the desk, Zhang Zhongyuan said, "To verify from the odd numbers, we need to consider the first odd number that is verified."
"It may be an odd number that is divisible by 3, or it may be an odd number that is not divisible by 3. However, after 3x+1, the second odd number reached, and the third odd number, the fourth, the fifth, and so on. Every odd number reached during the whole process must no longer be divisible by 3."
"But if we start from an odd number that is divisible by 3, then every odd number we reach on the way must no longer be divisible by 3, and will eventually come down to 1, so we must have traversed all the odd numbers."
As Zhang Zhongyuan continued to talk, the students' thoughts, which had just been pulled back from their thoughts, fell into deep thought .
Chen Zhou was still looking at Zhang Zhongyuan. He knew all of this and was still waiting for Zhang Zhongyuan's next words.
However, Zhang Zhongyuan obviously knew how to manage his time, and he did not immediately interrupt his classmates' thinking.
Chen Zhou felt someone touching him, and he turned his head to look at Zhao Qiqi in confusion.
Zhao Qiqi asked in a low voice: "Brother Chen, what does traversal mean?"
Chen Zhou was slightly stunned, and then explained: "Traversal is a concept in discrete mathematics, which means visiting each node which is what Professor Zhang calls arrival. Yes, this content is included in the book "Data Structure" in the sophomore year."
"Oh oh." Zhao Qiqi nodded repeatedly, feeling a little embarrassed.
He hasn't seen this textbook yet...
Chen Zhou's answer also provided an explanation for other students who did not know the word traversal.
Naturally, they turned and looked at Chen Zhou again.
There is admiration and envy in his eyes.
Although I know that Chen Zhou is already a participant in the final exams of each grade in the Department of Mathematics, it is a whole different feeling to truly feel this powerful strength.
On the podium, Zhang Zhongyuan glanced at the time and spoke again: "I just mentioned the odd numbers that are divisible by 3. I guess you have already thought of the odd numbers that are not divisible by 3."
"If we start from an odd number that is not divisible by 3, then every odd number we reach along the way will also not be divisible by 3, and they will all eventually come down to 1."
At this point, Zhang Zhongyuan glanced at Chen Zhou again before continuing, "In fact, in the verification process, odd numbers that are not divisible by 3 have an infinite number of odd numbers from the previous step."
"Among them, about 1/3 are odd numbers that are divisible by 3, and about 2/3 are odd numbers that are not divisible by 3. And what do you think this phenomenon resembles?"
As soon as Zhang Zhongyuan finished speaking, Chen Zhou stood up and said, "It's very similar to the situation with natural numbers."
After hearing what Chen Zhou said, Zhao Qiqi beside him suddenly realized: "Yes, it is very similar to natural numbers. Why didn't I think of it?"
Li Li glanced at Zhao Qiqi and said, "Do you want to know why?"
Zhao Qiqi: “Why?”
Li Li: "Because you don't read as many books as he does."
Zhao Qiqi was stunned, not understanding the meaning of this sentence. He muttered: "You might as well say that I'm not as smart as Brother Chen..."
Li Li glanced at him and stopped talking.
Instead, the classmate in front of Zhao Qiqi turned around, looked at him with complicated eyes and said: "I think this might be what he meant..."
Zhao Qiqi: “…”
Zhang Zhongyuan raised his hand to stop the noise, then motioned Chen Zhou to sit down. He continued, "Student Chen Zhou is right. This phenomenon is surprisingly coincidental with the situation of natural numbers."
After he finished speaking, he noticed that Chen Zhou was still standing there, so he asked, "Chen Zhou, do you have any questions?"
Zhang Zhongyuan's words also attracted the attention of all the students.
Under the gaze of everyone, Chen Zhou said softly: "Professor, this new verification method has obvious flaws."
Zhang Zhongyuan smiled and nodded: "Well, tell me about it?"
Zhang Zhongyuan's thought at this moment was that this kid stole the show in this small class.
But he didn't care.
After all, Chen Zhou has always been a student he values very much.
More importantly, this kid looks a lot like him when he was young...
Chen Zhou didn't think too much about it and said directly: "The calculation of this verification method is not continuous, which is very troublesome when verifying the climb or descent. When climbing, you need to factor 2, and when descending, you need to calculate 3 to the Nth power first."
After a pause, Chen Zhou continued , "Of course, this method also has its advantages. The advantage is that when it is verified to be almost infinitely climbing, it can be directly replaced. Well, let me give you an example."
When Zhang Zhongyuan heard Chen Zhou ask for an example, his eyebrows jumped, and he thought of the first time they discussed the topic.
At that time, Chen Zhou also gave an example to supplement Shen Jing's research ideas...
However, Chen Zhou's voice brought Zhang Zhongyuan's thoughts back to the classroom.
"For example, the verification process of 2n-1 times 2 to the power of 100 million minus 1 is to replace 100 million 2s with 100 million 3s, which is 2n-1 times 3 to the power of 100 million minus 1. Through this one-time replacement, we need to calculate 3 to the power of 100 million."
"If we follow the traditional verification method, we need to calculate 2n-1 times 2 to the power of 100 million minus 1, and then calculate 100 million minus 1 steps to get this result."
When Chen Zhou finished speaking, the bell outside the classroom rang.
Zhang Zhongyuan glanced at the time. It was almost time. Chen Zhou's performance was over. It was time to leave get out of class...
After leaving a thinking question at the end: "Summarize the odd numbers that are divisible by 3 and the odd numbers that are not divisible by 3, and calculate them using the general formula", this small class officially ended.
