Science also crosses borders, and it is always everywhere in unexpected ways.
The seemingly dull sequence of numbers can present a dazzling scientific beauty. unbelief? Then let's join Cao Zexian, a teacher at the Institute of Physics of the Chinese Academy of Sciences, to understand the mythical fantasy of the Fibonacci sequence!
Natural numbers are infinite. If some numbers are arranged in a regular row, they constitute a sequence of numbers. Expressed as a function is a sequence of numbers.
Such as: even numbers 2, 4, 6, 8...
Odd numbers 1, 3, 5, 7...
Triangles 1,3,6,10,15....
Prime numbers (atoms) 2, 3, 5, 7, 11, 13, 17.
The function that concatenates the items of a sequence of numbers with a plus sign in turn is the series. The Fourier analysis technique developed by the Fourier series is the most powerful mathematical and physical tool. Don't believe it, unfolding the cost signature function series is the basic operation of quantum mechanics.
In human history, the Italian mathematician Leonardo Fibonacci was a genius who learned Arabic numerals as his father did business in North Africa at a young age. In 1202, he wrote the book Liber Abaci(Abaci), which spread the Indo-Arab number system to the West.
The Arabic numeral system makes mathematics and physics possible. Mathematics and physics are represented by Arabic arrays, Latin + Greek letters, which is a set of discourse systems that all those who want to engage in scientific research must master!
In the book "Liber Abaci "Arithmetic", Fibonacci asks an interesting question: there is a pair of adult rabbits, every other month to give birth to a pair of rabbits, and the rabbits after a month also become adults to join the ranks of rabbits, if each pair of rabbits go through such a process of birth, maturation, fertility, and never die, ask how many pairs of rabbits after N months? Let's use a treemap to show it:
Expressed as: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... Each item in the sequence is called a Fibonacci number, denoted by the symbol Fn. F(0)=1，F(1)=1, F(n)=F(n - 1)+F(n - 2)（n ≥ 2，n ∈ N）。
This is the famous Fibonacci sequence, also known as the "rabbit sequence".
It's interesting, but that's it? What does the Fibonacci sequence mean for human development?
Behind every mathematical and physical object is too much that we don't know, or we know or understand. We can't understand it, but scientists can.
In mathematics , Yanghui triangles are arrays of triangles that appear in probability theory , combinatoriology , and algebra as binomial coefficients. The Fibonacci sequence is related to the Yang Hui triangle (i.e., Pascal triangle), and the sum of the diagonal lines in the Yang Hui triangle is the Fibonacci number, as shown in the figure:
In 1611, the famous astronomer Kepler pointed out in the book Strena seu de Nive Sexangula (Hexagonal Snowflake) that the Fibonacci sequence converges on the golden section:
The Golden Section number hides mysteries. Whether it's mathematical calculations or physical research, there will always be golden section numbers that pop up coldly out of nowhere.
According to the Fibonacci sequence, take the squares with side lengths of 1, 1, 2, 3, 5, 8, 13, 21... respectively, draw a quarter curve with a vertex of each square as the center of the circle, and then connect all the curves, and the final spiral line is the "Fibonacci spiral" shown in the following figure:
The golden section is an important foundation of aesthetics. People carry out architectural design and artistic sculpture according to the golden ratio. From ancient times to the present, many mysterious buildings have followed the law of the golden section, such as the ratio of the sloped triangle height of the pyramid to the length of the half side of the bottom surface. The Venus of Beauty sculpture is a perfect display of the Golden Section. Artists don't have to know too much about mathematics, but they can't become qualified artists without understanding the golden ratio.
Fibonacci sequences have been found in various fields. The most typical fibonacci sequence application in life is in botany. When observing nature, human beings found that trees grow branches in the process of growth, and if we count the number of branches from bottom to top, we will find that they are 1, 1, 2, 3, 5, 8, 13... It just happens to be a Fibonacci sequence. Nature's flowers have their own beauty, but the total number of almost every petal will be chosen by the fibonacci series of numbers: 3, 5, 8, 13...
The leaf order in botany also perfectly conforms to the Fibonacci sequence. Leaf order is a study of the arrangement of botanical units (organs) on plants. The leaf arrangement of the plant is spiraling upwards, and the leaf sequence cycle of different plants shows the arrangement of the Fibonacci sequence.
In botany, fibonacci oblique spirals are also common. The Fibonacci oblique spiral can be seen as either a set of counterclockwise spirals or a set of clockwise spirals, in which case the number of spirals is two neighboring numbers in the Fibonacci sequence. The sunflower flower plates, pine nut seeds, and scales on pineapples that we are familiar with all fit this perfectly.
Some scientists speculate that the Fibonacci oblique spiral is a dense accumulation of identical units on the cone surface, which is conducive to the accumulation of plant seeds and reproduction. Therefore, nature contains infinite mysteries, and we must learn to look at her with mathematical and physical eyes. Insight into the mysteries of nature is a tribute to nature by human beings.
More than 800 years have passed, and the magical Fibonacci sequence has been continuously verified by humans, and has been widely used in computers, physics, chemistry and other fields, making this ancient sequence rejuvenated.
In computer programming, when recursive functions are mentioned in many C textbooks, fibonacci sequences are used as examples. Fibonacci sequences are also incorporated into mathematics curricula at all levels from elementary school to university.
In modern physics, according to the Fibonacci sequence, the quasi-periodicity of the three-dimensional physical space of the golden section, the silver fraction, and the platinum fraction can be calculated. In quantum mechanics, the entanglement of two particles and the study of quantum critical points are also inseparable from the Fibonacci sequence.
In the field of chemistry, stress engineering for inorganic materials reproduces the mystery of the diagonal spiral of the Fibonacci sequence. Fibonacci sequences are also widely used in stock markets to reveal the mysteries of stock fluctuations...
Source: Science and Technology Daily
Editor: Zhang Shuang
Review: Yue Liang
Final Judgement: Wang Yu