Chapter 35: Fibonacci Sequences and Taxi Numbers

The Fibonacci sequence, also known as the golden section sequence, was introduced by the mathematician Leonardoda Fibonacci (Leonardoda Fibonacci) using rabbit breeding as an example, so it is also called the "rabbit sequence", which refers to such a sequence of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34、...... Mathematically, the Fibonacci sequence is defined recursively as follows: F(0)=0, F(1)=1, F(n)=F(n-1)+F(n-2)(n≥2,n∈N*) In modern physics, quasicrystalline structure, chemistry and other fields, the Fibonacci sequence has direct applications, for this reason, the American Mathematical Society has published a mathematical journal named "Fibonacci Quarterly Series" since 1963 to publish research results in this area.

Of course, the Fibonacci sequence mentioned by Junxin is slightly different from the actual Fibonacci sequence. The actual Fibonacci sequence has a stipulation that the zero term is zero, the first term is one, and the subsequent terms are equal to the sum of the first two terms. Junxin's is different, he starts with the student numbers of two people, although the rules of operation are the same, but the relative items are completely different.

Junxin's suggestion was quickly approved by everyone. No matter what the era, people are always curious and positive about new games, let alone positively related to what they have learned. So much so that the resolution on the whole class that had been passed before was ruthlessly discarded at this moment. Of course, in addition to the party Junxin and the initiator Wu Zhe and other class cadres, they still remember this stubble.

Since the calculation is based on the Fibonacci formula, the later you go, the larger the value, and the calculation will be very troublesome. However, since the calculation only compares the last two digits, as long as the numbers on the first digits are automatically ignored each time, and the last two digits are retained, it is completely suitable for the current scene.

Because he is not familiar with the people in the class, and he does not know the information such as everyone's student number, he himself will not reduce or avoid the chance of being selected because of his strong mathematical calculation ability.

Soon, after re-discussion, Junxin's opinions were adopted and appropriately modified, and the implementation began. So the quick calculations began in this room. As a result, the first unlucky guy was quickly pumped out. 1729, such a unique and mundane data.

Junxin didn't know most of the people in the class, but the three people in the same dormitory and Wei Donglai, who used to ask him questions in class, were probably the four people Junxin was most familiar with. The first person who was drawn was one of the people Junxin knew, Wei Donglai, who was also famous in the classroom with the student number 1729.

Unlike Junxin, Wei Donglai's reputation is not because of how much he has done, but because of his experience of studying abroad and answering questions from teachers and other classmates in the class. Coupled with his American thinking habits and style, he has a very high popularity in the class.

"Junxin, if you accept your fate, why are you involved with me again?" Wei Donglai was very familiar with Junxin, and as soon as he stood up, he said with a smile to Junxin.

"It's clear that you're cheating on me, I'm sure I'll find a way to get rid of it!" Junxin said with a smile.

"But I don't know what to do!" Wei Donglai scratched his head and said with a little distress. Although he has a good personality, he is not the kind of person who is very literary and artistic, and it is nothing to roar when he is usually fine, if he really goes on stage to perform, it will be a joke.

In fact, this is also a common problem for mathematics and even science students. Not every science student is not only musically playful like Queen's guitarist Brian May, but also a Ph.D. in physics at Imperial College London. Of course, no one knows for sure that there may be a few scientists who are hiding it deeply. For example, Albert Einstein, the greatest theoretical physicist of the 20th century, was a famous violinist. But such people are only a minority after all.

"It's okay, think about it!" Junxin suddenly had a bad taste, "Maybe you have figured out that you are the next Albert Einstein!" ”

"Are you laughing at me?" Wei Donglai was not angry and glanced at Junxin. However, under the influence of foreign education, Wei Donglai did not flinch. Instead, I started thinking about it.

Jun Xin is actually very familiar with Wei Donglai, for no other reason, that is, Gu Mengxue often mentioned Wei Donglai's name when chatting with Jun Xin again. This made him pay more attention to Wei Donglai himself, and after a period of getting along, Junxin came to the conclusion that Wei Donglai was also a relatively outstanding genius of this era, and he was open-minded. Not confined to the old way of thinking, often has his own unique thinking about some issues, when Junxin communicates with him, there is always a unique feeling of going back to the past when he was in graduate school and chatting with his friends on a question in Princeton. So when interacting with Wei Donglai, he had a more casual attitude than others.

Taking advantage of Wei Donglai's free time to think hard, Junxin thought of Wei Donglai's student number, the meaning of the number 1729 in 1729.

As a mathematician, the most important trait is to be sensitive to numbers, in other words, to always be sensitive to any number.

The number 1729 is also a famous name in the history of mathematics, and Junxin naturally knows it very well? For ordinary people, 1729 is just an ordinary natural number between 1728 and 1730, but in the eyes of mathematicians, 1729 is a representation of the number of taxis.

1729 is mathematically a sum of cubes that can be written as two numbers in two different ways, and is the smallest of the numbers with this property. The next number with this nature is 4104.

The name taxi comes from a story told by the British mathematician Hardy about the Indian mathematician Ramanujan: "Hardy once took a taxi in London to visit Ramanujan, and when he got out of the car, he noticed that the license plate number was 1729, and he probably pondered the number, because when he walked into the ward where Ramanujan was hospitalized, he had not even said hello, and blurted out his disappointment at the number, which he said was a boring and boring number, and hoped it was not a bad sign." 'Hardy, you are wrong,' said Ramanujan, 'and it's a very interesting number. It is the smallest number that can be expressed in two different ways as the sum of two positive cubes. This is the origin of the number of taxis, because it is related to taxis, so it is also called the number of taxis, the number of taxis.

Because of Ramanujan's high sensitivity to numbers, people in the world often joke that all whole numbers are Ramanujan's friends.

Speaking of Ramanujan, one of the most famous mathematicians in Indian history, he came from a poor background and never received a formal education in mathematics, and the way this great god learned mathematics was by no means human. He bought a book with more than 5,000 mathematical theorems and formulas, and a thick notebook, and began to prove them one by one.

Later, he got married, got a job as a scribe in Chennai, and studied mathematical theorems independently. After some time, Ramanujan sent a long list of complex theorems to Cambridge University, and Professor Hardy, an academician of Trinity College and a representative of the British school of analysis with great influence in mathematics at that time, saw the light of wisdom in the theorems, brought him from India to Cambridge, and then began his journey against the sky!

Ramanujan quickly conquered the entire mathematical world with his talents, and Hardy lamented that he was an unborn genius. He designed a grading scale for his mathematical aptitude, and calculated his mathematical aptitude with 20 points, and Hilbert, the head of the Göttingen School, the largest school in mathematics at that time, could score 80 points, while Ramanuqiang had to score 100 points! Hilbert was the first person in the mathematical community at that time, and his status was comparable to that of Euler, Gauss and others.

At that time, Einstein was invited to give a lecture in Göttingen, where he had not yet fully mastered the equations of the field field, and Hilbert introduced the form of the action of the field equation before Einstein himself. From this, Hardy's evaluation of Ramanujan can be seen.

Later, Ramanujan really made great achievements in mathematics, and the formulas he left behind caused countless majors to compete for research, and in 1997 even a special journal, the Ramanujan Journal, was born to publish research papers on "the field of mathematics influenced by Ramanujan".