Looking at Aveline who was looking for advice humbly, Xu Yun's expression couldn't help but be a little subtle.
As we all know.
People have three major hallucinations:
Someone is looking for me,
I can fight back,
He/she likes me.
As a very talented person from later generations.
Although Xu Yun was not so narcissistic that the girl would confess to him, when he heard that the girl had questions to ask him, he still subconsciously thought that the other party would say something related to his background.
The result was unexpected...
Is the problem Aveline mentioned really a problem?
Fibonacci numbers.
This is a very, very famous mathematical mystery that is extremely useful in mathematics, life, and nature.
The Fibonacci sequence can be traced back to the 7th century AD, when there was an Indian mathematician named Gopala.
This person first described this sequence when studying the number of methods when the lengths of box packaging objects are exactly 1 and 2, which is the following problem:
There are n steps. You can only cross one or two steps at a time. How many ways are there to go upstairs?
Then the question changed again and became the more famous rabbit mystery:
Assuming that rabbits have the ability to reproduce after two months of birth, a pair of rabbits can give birth to a pair of baby rabbits every month.
If all the rabbits do not die, how many pairs of rabbits can be reproduced in one year?
This problem was finally reduced to a sequence by Fibonacci, that is:
0,1,1,2,3,5,8,13,21,34,55,89,144,233,377... Such an infinite sequence.
Its characteristic is that the last number is the sum of the first two numbers, 0 1=1, 1 1=2, 1 2=3 and so on...
And dividing the next number by the previous number, it is infinitely close to the golden section number 0.618.
If this sequence is expressed by a formula, it is Xn=X(n-1) X(n-2), where X0=0 and X1=1.
In the novel "The Da Vinci Code".
The curator of the Louvre was murdered and his body was left on the floor. At that time, the curator took off his clothes, posed as Leonardo da Vinci's famous painting Vitruvian Man and left some strange codes.
And these elusive codes are exactly the Fibonacci sequence.
The bee family tree in nature, the phyllotaxis of pine cones and even the shapes of melons and fruits are all related to the Fibonacci sequence. In 2005, Professor Cao Zexian cooperated with the Institute of Physics, Chinese Academy of Sciences, to study microorganisms with a diameter of about 10 microns using silver cores and silica shells.
Stresses in structures.
Finally, by manipulating the stress on the inorganic microstructure composed of silver core and silica shell, the Fibonacci spiral pattern was successfully produced.
The more you study mathematics and physics, the more you will marvel at the wonder of life.
correct.
Since we are talking about Professor Cao Zexian, here is a brief rumor.
Professor Cao Zexian is also a controversial celebrity. He is the chief scientist of the 973 Nanomaterials Project of the Ministry of Science and Technology and a leader at the Hundred Talents Plan level.
However, some outrageous opinions often come out of his mouth, some of which are true and some of which are false.
For example, he once said this in a lecture at the National University of Science and Technology:
"85% of mathematics and physics knowledge has not been introduced to China, and this knowledge is closely guarded by foreigners."
This sentence is actually a bit bluffing, a bit like arrogance deliberately made for people.
Everyone knows that there must be some knowledge abroad that has not been shared with us, but that content mainly covers the front-end field, and it is definitely not as outrageous as 85%.
So.
Another sentence that was spoken by him at the time to support the above point of view has also become a joke on the Internet:
"Don't you know, a triangle has a heart."
But in fact this sentence is correct and is a very formal mathematical research direction.
It’s just that it belongs to the conclusion of elementary plane geometry. Flat geometry has long ceased to be a research direction in front-end mathematics, and is basically useless to most people.
Therefore, it is not that this knowledge has not been introduced into the country, but it is meaningless to teach it - even the top competition classes of top foreign universities will not study these triangle hearts.
Generally speaking.
Ordinary people only need to master the five types of mind, while those who study geometry can only master 50 types at most.
What follows is almost purely theoretical, extremely unpopular and remote.
Therefore, Professor Cao used this example to prove that "85% of mathematics and physics knowledge has not been introduced to China" is not correct, but there is nothing wrong with the number itself.
It is not anti-intellectual, let alone civil science, because the determination of the triangle heart is that the three lines have the same point, and there are too many hearts locked by this.
There is currently a website that collects all these thoughts together, and the website address is fasville.edu/cyclopedia/ETCPart4. (This is a professor of volute after all, and the content he talks about is easy to laugh at, but this data is indeed correct.
)
OK, let’s return to the original topic.
The Fibonacci sequence is widely used in life and mathematics, and what are the perfect square terms in it has always been a very contradictory question.
What is called a perfect square number.
It refers to the form in which a number can be expressed as the square of an integer.
For example, 4=2^2, 9=3^3, 256=4^4, etc...
Why is the perfect square term in the Fibonacci sequence a very contradictory issue?
the reason is simple.
This problem was not calculated by the British mathematician J. H. E. until more than fifty years before Xu Yun traveled through time, that is, in 1964.
Judging from the time point, it is undoubtedly a difficult problem that has only been solved in modern times.
But at the same time.
Its cracking process uses elementary number theory content and the same properties as the prime number theorem and the four-color theorem.
This is also one of the very few mathematical problems that can be solved using elementary number theory. In theory, it could have been solved in 1800.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! Of course.
The very few examples in the past did not include Ge Guess - if you are lucky, you can see thousands of elementary proofs of Goldbach's conjecture produced by civil scientists at home and abroad every year...
But just like physics can be divided into classical physics and more microscopic quantum physics.
J. H. E. ...that is, the perfect square term proved by Cohen is only an answer within a certain range, and it is generally accepted that it is the range of the first 200,000 Fibonacci numbers.
If the range is expanded infinitely, several more perfect square terms can still be found.
For example, the fourth number is approximately at the position of .
After that there are 6.1613e 030, 9.9692e 030 and so on...
This is also within the scope of theoretical research. For Aveline at present, it is enough to use Cohen's problem-solving method.
Then Xu Yun took the paper and pen and began to calculate while talking:
"First we define a Lucas sequence, which is the Fibonacci sequence, Xn=X(n-1) X(n-2), but X belongs to N, N≥3..."
"Then generalize the domain from the natural number set to the integer set..., we can get 2F_{m n}=F_{m}L_{n} F_{n}L_{m}...
"
"Let m=1, we can get 2F_{n 1}=F_{1}L_{n} F_{n}L_{1}....Thus 2L_{m n}=5F_{m}F_{n} L_{
n}L_{m}......"
"Then go in and out like this (mathematical induction method)...accelerate and decelerate (quadratic remainder)...and then polish it a little more (Eulerian discrimination method), touch it twice from this position (tossing and turning
division method)...then nine shallow and one deep (modulo periodic sequence)..."
More than ten minutes later.
"...To sum up, 1,1,144 is the only perfect square term in the Fibonacci sequence!"
Xu Yun put down his pen, took a deep breath, and said to Aveline:
"Done!"
Aveline took the calculation paper and read it carefully.
Xu Yun leaned on the bench and wiped the sweat from his forehead in the blind spot of Aveline's field of vision.
Finally got it done...
It should be moisturized next, right?
However, just when Xu Yun thought he had passed the test, Aveline's voice suddenly sounded in his ears again:
"Classmate Luo Feng, when did you solve the problem of the perfect square term in the Fibonacci sequence?"
Xu Yun's mentality was relatively relaxed at this time, and he subconsciously opened his mouth after hearing this:
"Nineteen......"
But before he finished speaking, he suddenly woke up. He quickly sat up straight and said with a dry laugh:
"Classmate Aveline, look at what you said, the problem I solved..."
"This is the calculation result I discovered from the manuscript left by my ancestor Fat Fish when I was nineteen years old."
Aveline glanced at him with a half-smile and confirmed:
"Are you telling the truth?"
Xu Yun had a vague premonition in his heart, but now that the words were spoken, there was no reason to take them back:
"Of course it's true. I'm an honest young man who claims to make 30,000 updates a day..."
Aveline looked at him quietly for a few seconds, then suddenly took out two manuscripts from her body and handed them to Xu Yun:
"Then look at this."
Xu Yun subconsciously took the manuscript, put it in front of him and started reading.
The first manuscript seems to be a bit old, and the handwriting is messy. It has a somewhat unrestrained feel, but it has an inexplicable sense of familiarity.
The handwriting on the second manuscript was much more elegant and neat, and Xu Yun recognized it as Aveline's handwriting at a glance:
On Christmas Day, everyone wrote down their future expectations in their diaries. Xu Yun's memory was still fresh in Aveline's handwriting and content.
In addition to the difference in handwriting between the two manuscripts, the content on them made Xu Yun's eyes widen:
Although the methods of solving the problems are different, they are all demonstrating the problem of the perfect square term in the Fibonacci sequence!
Among them, the method of the first manuscript is relatively primitive, and the starting point is Fermat's Little Theorem.
Then it was transformed through the Taylor formula of n-th unit root, and "self-study" produced a relatively primitive odd prime number check logic.
"Swallowing the Starry Sky: Sign in to Become a God"
Aveline's derivation process is relatively simple in terms of tools, but the steps are a little cumbersome.
There are some parts of her process that could be simplified, but the main idea is the same as Xu Yun...
Totally consistent!
no doubt.
Even before Xu Yun spoke, Aveline had mastered at least two problem-solving methods.
Seeing Xu Yun swallowing saliva, Aveline continued to mend the knife:
"Classmate Luo Feng, if you see it, the first manuscript is the derivation process left by Newton's ancestors, and the second manuscript is my bad work."
"Euler was less than 20 years old when our ancestor Newton was alive, and he was far from deriving Euler's criterion."
"So although he solved the problem in the Fibonacci sequence, he only used a logical tool he created, and other ideas were relatively primitive."
"At the same time, ancestor Newton and Mr. Fat Fish were both teachers and friends. He loved to compete with Mr. Fat Fish in everything, so he once left a sentence after calculating this result..."
As she spoke, Aveline looked up at Xu Yun and said:
"He said, 'If that guy Fat Fish can also solve this problem, the only way is to use Han Li to develop a logic tool by himself like me.'"
"And in your calculation process, you made extensive use of Euler's discriminant method, which was only summarized by Euler in 1757..."
"...."
Xu Yun was silent for a few seconds, feeling that he should save himself again:
"Classmate Aveline, couldn't it be possible that the ancestor of Fat Fish deduced this rule before Euler?"
This chapter is not finished yet, please click on the next page to continue reading the exciting content! Aveline shook her head, took out an older manuscript from her body, and said:
"Ancestor Newton once encountered a huge bottleneck when calculating infinite magnitude. At that time, Mr. Fat Fish once proposed a quadratic approximation formula, which is this."
Xu Yun was slightly stunned and took the manuscript paper.
There is not much content on the paper, only a formula:
V(r)≈[V''(re)/2!](r-re)^2. (Chapter 32, put away the foreshadowing, buried 1.5 million words, let me put my hands on my hips for a while
, but it’s awesome)
Aveline saw this and added:
"It can be seen from this formula that Mr. Fat Fish's idea does not follow the law of quadratic reciprocity, and is completely different from Euler's system."
"You should know that for a mathematician, the thinking system is not something that can be easily changed."
After saying that, she took back her manuscript from Xu Yun's hand and shook it in front of Xu Yun:
"In addition, your and my derivation processes are almost the same. The whole process has an obvious color of the post-Euler era, and it cannot be the result of a hundred years ago."
"so......."
Aveline's eyes were as translucent as gems in the warm sun, and her ethereal voice struck Xu Yun's heart directly:
"Including some of the previous experimental designs, quite a few of them were actually made by you. Am I right?"
"..."
Xu Yun was silent.
be honest.
Ever since Aveline discovered the flaw in the name of the photovoltaic effect, he has actually been trying to avoid overturning it again.
For example, the relativity equations he gave Gauss, and various aspects of cathode rays, etc., have all undergone a lot of magical modifications...
But the problem is...
Most of the content he covered in the experimental session was related to physics.
But this time Aveline raised a mathematical question.
You must know that most physical knowledge can be divided into stages.
for example.
The previously mentioned Lorentz force formula f=qVBsinθ.
Before this formula was generalized in 1895, unless you were a time traveler, it was impossible to calculate the Lorentz force under certain conditions.
But math is different.
Many concepts in mathematics are incremental.
That is to say, before a certain formula is summarized, you actually have a certain chance to find its prototype.
For example, how much work A completed in a certain interval, B added after him, and finally C spread this rule to a larger range - such as a set of integers, etc.
So at least for a physics guy like Xu Yun.
You ask him to consider whether Euler's judgment has been established when solving elementary number theory. This is actually a very difficult and detailed issue.
Requires high mathematical sensitivity.
If he had enough time to think or was around, it would be better, and there might be a higher probability of getting a patch or something.
But Aveline appeared too suddenly today, and the initiative of the topic was not in Xu Yun's hands.
Therefore, successive factors coincided, and Xu Yun once again made a huge, huge, super, super mistake this time:
He used the derivation system of Euler's discriminant method, which is a related method that he learned later.
So he was possessed by Xiao Heizi and exposed his chicken feet...
Looking at Aveline with a determined look in front of him, Xu Yun couldn't help but pick up the "Classic Physics" in her hand.
If she denies it, will this girl let herself feel the power of knowledge?
Moreover, as far as the current situation is concerned, it actually makes no difference whether you deny it or not...
Think of this.
Xu Yun couldn't help but sigh quietly, and nodded his head very bachelorly:
"Um."
Hear this answer.
A smile suddenly appeared on Aveline's face.
The curvature of the corner of the mouth is as perfect as a crescent moon, like a ripple on the face, quickly crossing the face:
"It seems... I guessed it right. You are actually a genius, a real genius, right?"
.........
－－－－－－Digression－－－－－
I would like to recommend a new book for veterans, that is, those who hold a ruler in their hands, "Dr. Chen, Don't Be a Coward!", one of the few medical articles, this one is about Chinese medicine. There are really not many Chinese medical articles these days.
