Into Unscientific Chapter 314

  Chapter 314 Avelyn's Intuition (Part 2)

   On the bench.

  Looking at Avelyn who was humbly asking for advice, Xu Yun couldn't help but feel a little subtle.

   Well known.

  People have three major illusions:

   Someone is looking for me,

  I can fight back,

  He/she likes me.

  As a person who is a descendant who is very promising.

  Although Xu Yun was not so narcissistic that the girl would confess to him, when he heard that the girl had a question to ask himself, he more or less subconsciously thought that the other party would say something related to his background.

   The result was unexpected.

   Is the problem Avelyn said really a problem?

  Fibonacci sequence.

   This is a very, very famous mathematical puzzle that is extremely useful in both mathematics and life and nature.

  The Fibonacci sequence can be traced back to the 7th century AD, when there was a mathematician named Gopala in India.

   This person first described this sequence when studying the number of methods when the lengths of the box packaging objects are exactly 1 and 2, which is the following problem:

  There are n steps, and 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 advanced to the more famous rabbit puzzle:

  Assuming that rabbits are capable of reproduction after two months of birth, a pair of rabbits can give birth to a pair of young rabbits every month.

  How many pairs of rabbits can be bred in one year if none of the rabbits die?

  This problem was finally summarized into 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 latter number is the sum of the first two numbers, 0+1=1, 1+1=2, 1+2=3 and so on.

  And divide the next number by the previous number, it is infinitely close to the golden section number 0.618.

  If this sequence is expressed in 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 killed and his body was left on the floor. At that time, the curator took off his clothes, placed him in the Vitruvian Man, a famous painting by Leonardo da Vinci, and left some strange codes.

  And these elusive passwords are the Fibonacci sequence.

In nature, the bee family tree, pinecone phyllotaxy, and even the shape 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 microstructures with a diameter of about 10 microns using silver cores and silica shells. in the stress.

  Finally, the Fibonacci spiral pattern was successfully generated by manipulating the stress on the inorganic microstructure composed of silver core and silica shell.

  The more you study mathematics and physics, the more you will marvel at the wonder of life.

correct.

  Since Professor Cao Zexian is mentioned, here is a simple rumor by the way.

  Professor Cao Zexian is also a very controversial celebrity. He is the chief scientist of the 973 nanomaterials project of the Ministry of Science and Technology, and a leader at the level of the Hundred Talents Program.

  However, some outrageous opinions often come out of the mouth, some of which are true and some are false.

  For example, he once said such a sentence in a lecture at the National University of Science and Technology:

   "85% of the knowledge of mathematics and physics has not been introduced to China, and this knowledge is tightly held by foreigners."

  This sentence is actually a bit of a bluff, a bit of a deliberate and outrageous taste.

  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 then.

   Another sentence that was uttered with him at the time and used to support the above point of view became a joke on the Internet:

   "You don't know, there are 44072 hearts in a triangle."

   But in fact this sentence is correct, and it is a very formal direction of mathematical research.

   It's just that it belongs to the conclusion of elementary plane geometry. Pingji has long been no longer the research direction of front-end mathematics, and it is basically not used by most people.

  So it's not that this knowledge has not been introduced into China, but it's meaningless to teach it—even the top competition classes of top foreign universities will not conduct research on these triangle hearts.

  Generally speaking.

  Ordinary people only need to master the five minds, and those who learn geometry can master at most 50 kinds of minds.

   Beyond that, it almost belongs to the category of pure theory, which is extremely unpopular and remote.

  So Professor Cao used this example to prove that "85% of mathematics and physics knowledge has not been introduced to China" is not correct, but the number itself is not a problem.

   It's not anti-intellectual, let alone civil science, because the judgment of the triangle heart is that the three lines have the same point, so there are too many hearts locked.

   There is currently a website that collects these hearts together at faculty.evansville.edu/ck6/encyclopedia/ETCPart4. (After all, this professor is a volute, and the content of the mouth is flat, but the data is indeed correct)

  OK, the topic will return to the original place.

  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.

  The so-called perfect square number.

   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 it said that the perfect square term in the Fibonacci sequence is a very contradictory question?

the reason is simple.

  This problem was not calculated by the British mathematician J.H.E.Cohn until Xu Yun traveled more than 50 years ago, that is, in 1964.

  From the point of view of time, it is undoubtedly a difficult problem that has only been solved in modern times.

but in the meanwhile.

  Its cracking process uses the content of elementary number theory, which is the same property as the prime number theorem and the four-color theorem.

   This is also one of the very few mathematical problems that can be solved with elementary number theory. In theory, it could actually be solved in 1800.

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 conjectures born from the hands of domestic and foreign minkes every year.

   But just like physics can be divided into classical physics and more microscopic quantum physics.

  J.H.E.Cohn, that is, the perfect square term proved by Cohn is only an answer within a certain range, and it is generally recognized that the range of the first 200,000 Fibonacci numbers.

  If the scope is infinitely expanded, then several more perfect square terms can still be found.

  For example, the fourth number is 884358447525575649, which is about 1056412078.

   Further down there are 6.1613e+030, 9.9692e+030 and so on

   This also belongs to the scope of theoretical research. For the current Avelyn, using Cohen's problem-solving method is enough.

   Then Xu Yun took the paper and pen, and began to calculate while speaking:

   "First of all, let's define a Lucas sequence, which is the Fibonacci sequence, Xn=X(n-1)+X(n-2), but X belongs to N, N≥3"

   "Then extend the definition domain from the natural number set to the integer set. 2F_{m+n}=F_{m}L_{n}+F_{n}L_{m}"

"If m=1, we can get 2F_{n+1}=F_{1}L_{n}+F_{n}L_{1} and thus 2L_{m+n}=5F_{m}F_{n}+L_ {n}L_{m}”

"Then go in and out like this (mathematical induction method) to accelerate and decelerate (quadratic remainder). Then polish it a bit (Euler's discriminant method), touch it twice from this position (rolling and dividing method) and 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 Avelyn:

   "Done!"

   Avelyn took the math paper and looked at it carefully.

  Xu Yun leaned back on the bench and wiped the sweat from his forehead in the blind spot of Aveline's vision.

   Finally got it done.

   It should be possible to moisten it next, right?

  However, just when Xu Yun thought he had passed the test, Avelyn's voice suddenly sounded in his ears:

   "Student 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 when he heard the words:

"Nineteen"

  But before he finished speaking, he suddenly came to his senses. He sat up straight quickly, and said with a dry smile:

   "Student Avelyn, look at what you said, what is the problem I solved."

   "This is the calculation result I found in the manuscript left by the ancestor of Fat Fish when I was nineteen years old."

   Avelyn glanced at him with a half-smile and confirmed:

   "What you said is true?"

   Xu Yun had a bad premonition in his heart, but now that the words have been spoken, there is no reason to take them back:

   "Of course it's true, I'm a sincere young gentleman who claims to change 30,000 a day."

  Aveline watched him quietly for a few seconds, then suddenly took out two manuscripts from her body and handed them to Xu Yun:

   "Then you look at this."

  Xu Yun subconsciously took the manuscript, put it in front of him, and began to read it.

  The first manuscript seems to be a bit old, the handwriting is messy, and it has a taste of letting go, but there is an inexplicable sense of familiarity.

  The handwriting of the second manuscript was much more delicate and neat. Xu Yun recognized it as Avelyn's handwriting at a glance:

  Everyone wrote down their future expectations in diaries on Christmas Day, and Xu Yun still remembers Avelyn's handwriting and content.

   Besides the difference in handwriting between the two manuscripts, Xu Yun's eyes widened because of the contents above:

  Although the problem solving methods are different, they are all demonstrating the perfect square term in the Fibonacci sequence!

  The method of the first manuscript is relatively primitive, and the starting point is Fermat's little theorem.

   Then it was transformed through Taylor's formula of n times unit root, and "self-taught" produced a relatively primitive odd prime number check logic.

  Aveline's derivation process is relatively simple in terms of tools, but the steps are a little cumbersome.

  Her process can be simplified in some places, but the main idea is the same as that of Xu Yun

   Exactly!

no doubt.

  Even before Xu Yun spoke, Avelyn had mastered at least two methods of solving problems.

   Seeing Xu Yun swallowing saliva, Avelyn continued to add the knife:

   "Student Luo Feng, if you can see it, the first manuscript is the derivation process left by Newton's ancestors, and the second is my bad work."

   "Euler was less than 20 years old when Newton's ancestor was alive, and he was far from deriving Euler's discriminant method."

   "So although he solved the problem in the Fibonacci sequence, he only used a logical tool created by himself, and other ideas are relatively primitive."

   "At the same time, Ancestor Newton and Mr. Fat Fish are both teachers and friends, and they love to compete with Mr. Fat Fish in everything, so he once left a sentence after calculating this result"

   Speaking of which, Avelyn looked up at Xu Yun, and said:

   "He said, 'If Fat Fish can solve this problem, the only way is to develop a logical tool through Han Li's self-study like me.'"

   "In your calculation process, you have used Euler's discriminant method extensively. This is the method that Euler induced in 1757."

   Xu Yun was silent for a few seconds, feeling that he should save himself again:

   "Student Avelyn, couldn't it be that the ancestor of Fat Fish deduced this rule before Ola?"

   Avelyn shook her head, took out an older manuscript from her body, and said:

   "Ancestor Newton once encountered a huge bottleneck when calculating the infinite magnitude. At that time, Mr. Fat Yu once proposed a quadratic approximation formula, which is this."

  Xu Yun was slightly taken aback, then took the manuscript paper.

  There is not much content on the paper, only a formula is listed:

  V(r)≈[V''(re)/2!](r-re)^2. (Chapter 32, close the foreshadowing, buried 1.5 million words, let me have a hip for a while, but it's awesome)

  Aveline added upon seeing this:

   "From this formula, it can be seen that Mr. Fat Yu's thinking does not follow the law of quadratic reciprocity, and it 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 speaking, she took back her manuscript from Xu Yun, and shook it in front of Xu Yun:

   "In addition, your derivation process and mine are almost the same. The whole process has an obvious post-Euler color, and it is absolutely impossible to be the result of a hundred years ago."

"so."

  Aveline's eyes were as bright as jewels in the warm sun, and the ethereal voice hit Xu Yun's heart directly:

   "Including some of the previous experimental designs, quite a few are actually from your own hands, am I right?"

  Xu Yun was silent.

be honest.

  Ever since Avelyn discovered the loophole in the name of the photovoltaic effect, he has actually been avoiding another rollover.

  For example, the relativity equation he gave Gauss, and various links in the cathode ray, etc., have undergone a lot of magical changes

   But the problem is

  Most of the content he involved in the experimental session was related to physics.

   But what Avelyn raised this time was a math problem.

  You must know that most of the physical knowledge can be divided into stages.

for example.

  The previously mentioned Lorentz force formula f=qVBsinθ.

  Before this formula was summarized in 1895, unless you were a traveler, it was impossible to calculate the Lorentz force under certain conditions.

   But math is different.

  Many concepts in mathematics are incremental.

   That is, before a certain formula is summarized, you actually have a certain chance to find its prototype.

  For example, how much work A has done in a certain interval, B has added after him, and finally C has spread this law to a larger range—such as an integer set and so on.

  So at least for a physicist like Xu Yun.

  You ask him to consider whether the Euler judgment has been established when solving elementary number theory. This is actually a very difficult detailed problem.

   Requires high mathematical sensitivity.

  If he has enough time to think or be around, it's better, maybe there is a higher probability of a patch or something.

  But Avelyn appeared too suddenly today, and Xu Yun didn't take the initiative to talk about it.

  Thus, the successive factors coincided, and Xu Yun made another huge, huge, super super super mistake this time:

  He used the derivation system of Euler's discriminant method, which is the related method he learned later.

  So he was possessed by Xiao Heizi, showing his chicken feet.

  Looking at Avelyn with a determined face in front of her, Xu Yun couldn't help but click the "Classical Physics" in her hand.

  If she denies it, won't this girl let herself feel the power of knowledge?

  Besides, as far as the current situation is concerned, there is actually no difference whether you deny it or not.

  Think here.

  Xu Yun couldn't help but sighed faintly, and nodded his head very bachelorly:

"Um."

   Hear this answer.

   A smile suddenly appeared on Avelyn's face.

  The curvature of the corner of the mouth is as perfect as a crescent moon, like a ripple on the face, quickly across the face:

   "Look. I guessed right, you're actually a genius, a real genius, right?"

   Recommend a book, the old hand is the new book with an inch in hand, "Doctor Chen, don't be cowardly!" 》, one of the few doctors' texts at the starting point, this book is still about Chinese medicine. There are really not many Chinese medicine texts these days

  (end of this chapter)

Chapter end