The next morning, downstairs in the community, Chen Jie was waiting for Gao Geli to go downstairs. Since the two friends knew that each other lived upstairs and downstairs, they went to and from school together every day. The weather was good today, and the air was filled with the smell of the morning sun, but Gao Ge stood down a little later than usual, Chen Jie saw his sleepy eyes, and said with concern: "Didn't you sleep well last night?" ”

Gao Geli sighed and said: "Don't mention it, I was so angry that I almost didn't smash the computer last night, and I seem to have a premonition of my tragic fate in the future......"

"What's so serious?"

"Have you heard python? A programming language. After installing the python compilation environment yesterday, it couldn't run at all, and the result was debugged until 3 o'clock in the middle of the night, and I slept for less than 3 hours today, and I'm sleepy and crazy now!! ”

Chen Jie saw Gao Geli's dark circles, nodded sympathetically, and said, "Deeply sympathetic, has the problem been solved in the end?" ”

"Of course, don't look at who I am!" Gao Geli patted his chest proudly and immediately made a grimace disgusted by himself, "But do you know how I solved it? I downloaded last night's installation package from a third-party website.,In the morning, I went down an official website installation package.,Found that md5 doesn't match.,Later, I found out that I installed a 64-bit python compiler last night.,But my computer is a 32-bit ......"

"Although I don't know a lot about computers, I have the impression that a 32-bit operating system will directly report an error when installing 64-bit software, right? How can you still install it successfully? ”

"That's normal, but I suspect that the package I downloaded last night has been modified, so I put it on in a daze, but it doesn't work...... It's too bad! If I do this in the future, I don't know how many things like this kind of eating flies will encounter...... It's inexplicably sad to think about. ”

"If you feel sad, you will change your career. Say a lot, your computer better kill the poison. ”

"I already clicked on the anti-virus task before I went out, and now I'm running." Gao Geli pondered for a while after speaking, and continued, "Actually, I also understand that every line has its own difficulties, and I just complain and complain, and on the whole I still like the profession of code farmer." ”

"What attracted you to this line of work? There are not a few middle-aged siege lions. ”

"A sense of accomplishment! Writing a program is like finishing a work of art, and that feeling of satisfaction when it runs out as you expected...... What is the title of the gold list, what is the candle in the cave room, it is not worth mentioning at all! After speaking, Gao Geli opened his personal homepage with Chen Jie's mobile phone, opened a picture and handed it to him, "This is the first program I wrote in python, a golden spiral." ”

Chen Jie glanced at it, pursed his lips and nodded, half-jokingly: "Your program still has images, it's very advanced!" Isn't the first test program of the program ape 'Hello World'? ”

"'Hello World' is so low, how can that kind of program be embarrassed to show others?!"

As they were talking, the two happened to pass by a small supermarket, Chen Jie said: "I slept a little late last night, let's buy a can of Red Bull to refresh myself, I don't want to be called up by the teacher again because of dozing." ”

Gao Geli directly shook his head and refused: "If you want to buy it, you can buy it, I've seen it, today's first period is a math class, high school math is too simple, it doesn't matter if I listen to it or not, just use the first class to make up for sleep......"

……

……

In the first period, math class, Gao Geli fell asleep as promised, and Chen Jie barely supported himself with a refreshing drink.

Chen Jie's math teacher is a male teacher surnamed He who walks vigorously and resolutely, I heard that he has just graduated a few years, so he looks very young, giving people a feeling of vitality, and the speed of speech is much faster than that of the older teacher, the appearance is white and well-proportioned, and he usually likes to wear a half-sleeved T-shirt, and sometimes there is a little femininity between his gestures.

However, unlike in the past, today's Teacher He seemed to have a hint of mystery on his face when he came in, and after entering the class, he didn't shout for class and wrote the question on the blackboard alone. After writing the question, he glanced at the entire class with a blank face and said, "Today I want to do a thorough investigation, this question will give you 15 minutes, and we will talk about it in 15 minutes...... Who's the one in the back! I went to bed after the first class! Yes, that's you! Teacher He pointed to Gao Geli and said, "You come up and write this question." ”

"Huh?" Gao Geli walked towards the podium with a reluctant face, Chen Jie looked at his back and snickered, and said in his heart I have already reminded you, who told you not to listen?

Just as the whole class was concentrating on reviewing the problem, two of them had a weird smile on their faces, one was Chen Jie, who had just finished studying Eliot's theory, and the other was Gao Geli, who used python to draw the golden spiral, and a voice appeared in their hearts almost at the same time: "Isn't this the general formula for finding the Fibonacci sequence?!" ”

The basis of Eliot's theory that Chen Jie recently read is the Fibonacci sequence, and he has long figured out how to find the formula for general terms. Gogli's golden spiral itself was iterated using the general formula of the Fibonacci sequence, and he certainly knew how to find it. Looking at the questions that are fed to his mouth, Gao Geli's idea is very simple: the pending coefficient method is Gaveda's theorem, and Chen Jie's idea is also very simple: the characteristic root Gaveda theorem.

In less than two minutes, Gao Geli and Chen Jie completed their answers, and Mr. He carefully reviewed Gao Geli's board book with his hand on his chin, and was quite satisfied with his overall performance, but frowned imperceptibly while nodding.

After 10 minutes, many students in the class have made answers one after another, and Mr. He reviewed their derivation process one by one, still without a very satisfied smile on his face.

After returning to the podium, Mr. He said bluntly: "I am very satisfied with the fact that your answers are all correct, but you have not presented the most important thing I want to see, including the student next to the blackboard." In fact, your general direction is the same, that is, to find the general term formula by transforming it into a proportional series, but I would like to see you give a proof: how can you conclude that this sequence can be written as the sum of two proportional sequences? ”

Gao Geli thought it was a big deal when he heard it, so he replied: "Hey, teacher, you want to see this proof earlier, isn't your question the Fibonacci sequence, it is 'the second order constant coefficient homogeneous linear recursive sequence', it has a special solution, and the special solution is the sum of two proportional sequences, so of course it can be expressed by the proportional sequence." ”

"Yo ......" Mr. He was very surprised to hear the term "second-order constant coefficient homogeneous linear recursive sequence" from the mouth of a high school student, and he asked Gao Geli with a smile: "Then can you give a proof?" ”