1. Mathematically, the recursive formula of Peibonahi series is F(n)=F(n- 1)+F(n-2). After a series of mathematical deduction, we can find that the limit of Peibonahi series is the golden ratio of 0.6 18, the golden ratio in financial engineering and the golden ratio in construction engineering.
2. In computer algorithms, Fibonacci sequence is often used to solve some algorithmic problems, such as Fibonacci heap and Fibonacci search. Generally speaking, Peibonahi series is not only a mathematical structure, but also a set of laws and a way of thinking. Fibonacci sequence is also widely used in algorithm design and analysis, such as optimizing the efficiency of computer programs and improving image compression algorithms.
3. Musically, the rhythm of Peibonahi sequence has a special aesthetic feeling; In architectural design, such as rotating shell and spiral staircase, the proportion of Peibonahi series is borrowed; For example, in painting, the German painter Albrecht Dürer's "Mother-child Inverted Painting" adopted the Peibonahi sequence rule. All these performances can show the artistic value and cultural connotation of Pei Bonachi's sequence.
Brief introduction of Fibonacci sequence;
1, Fibonacci sequence is an infinite integer sequence defined recursively. The sequence starts with 0 and 1, and each subsequent item is the sum of the first two items. Fibonacci sequence was first proposed by Italian mathematician Leonardo Fibonacci in 1202 to describe the problem of rabbit reproduction.
2. Suppose a pair of newborn rabbits start breeding from the second month, and they can have a pair every month, and the rabbits will not die. How many pairs of rabbits will there be in n months? Through recursion, it can be concluded that the total number of rabbits in the nth month is n+ 1 term of Fibonacci sequence.
3. The constant of Peibonahi sequence tends to the golden ratio, and mathematicians further expand the theoretical structure of Peibonahi sequence. For example, in matrix theory, there is a kind of matrix F that is similar to Peibonahi sequence, and each term is related to the sum of its first two terms, so the formulas and properties similar to Peibonahi sequence can be deduced.
4. In multivariate number theory, Peibonachi sequences have similar problems. For every positive integer n, there is a problem that a group of integers (x, y) satisfy x 2-x * y+y 2 = n. The solution of this problem is related to Peibonachi sequence and modular operation. These expansion problems show that Peibonachi sequence has richer theoretical and practical connotations and is worth further study.