(Resource: https://en.wikipedia.org/wiki/Fibonacci_number)

什么叫斐波那契数？像 0，1，1，2，3，5，8，13，21，34，55, 89, 144, 233, 。。。这样的数，就叫斐波那契数，每个斐波那契数等于前面两个斐波那契数的和 (0是第零項)。前後兩項之比 1/2 , 2/3 ,  3/5 , 5/8 , 8/13 , 13/21 , 21/34 ,...... (的小数部分)會趨近黃金分割0.618。大家不妨对自己的脸，自家后院的玫瑰花。。。用斐波那契数进行黄金分割分析：

斐波那契数依然还有许多问题等待您去研究，例如(https://en.wikipedia.org/wiki/Fibonacci_number):

1. 斐波那契數列中是否存在無窮多個質數？

   在斐波那契數列中， 有質數： 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917, 475420437734698220747368027166749382927701417016557193662268716376935476241, …… 目前已知最大質數是第81839個斐波那契數，一共有17103位數。[A Fibonacci prime is a Fibonacci number that is prime. The first few are:  2, 3, 5, 13, 89, 233, 1597, 28657, 514229, ... OEIS: A005478. Fibonacci primes with thousands of digits have been found, but it is not known whether there are infinitely many]

2. It is not known whether there exists a prime p such that

    

3. Determining a general formula for the Pisano periods is an open problem.

    

References:

[1] 美国数学会从1963年起出版了以《斐波纳契数列季刊》为名的一份数学杂志，用于专门刊载这方面的研究成果。https://en.wikipedia.org/wiki/Fibonacci_Quarterly (https://www.fq.math.ca/list-of-issues.html)dealing directly with topics that are very closely related to Fibonacci numbers, such as Lucas numbers, the golden ratio, Zeckendorf representations, Binet forms, Fibonacci polynomials, and Chebyshev polynomials. However, many other topics, especially as related to recurrences, are also well represented. These include primes, pseudoprimes, graph colorings, Euler numbers, continued fractions, Stirling numbers, Pythagorean triples, Ramsey theory, Lucas-Bernoulli numbers, quadratic residues, higher-order recurrence sequences, nonlinear recurrence sequences, combinatorial proofs of number-theoretic identities, Diophantine equations, special matrices and determinants, the Collatz sequence, public-key crypto functions, elliptic curves, fractal dimension, hypergeometric functions, Fibonacci polytopes, geometry, graph theory, music, and art.

[2] https://en.wikipedia.org/wiki/Fibonacci_number, https://www.mathstat.dal.ca/fibonacci/, https://baike.baidu.com/item/斐波那契数  

[3] http://szes.cau.edu.cn/art/2017/9/29/art_27800_533062.html:  在自然界中到处可以发现这个数列的应用。向日葵的种子在花盘上的排列呈现不同方向的行与列，总行数和总列数是这个数列的相邻两项的数值，小一点的为55和89，大一点的为89和144。松果球种子排列的行列数一般为5和8，菠萝鳞片的行列数一般为8和13。罗马花椰菜的各级小花排列也都符合这一数列。其实这些现象并非巧合，它所反映的是生长的一般规律，如兔子的繁殖、小麦分蘖的发生、细胞的分裂、叶片的生长等，甚至是微观世界的分子DNA结构也遵循着这一规律。

[4] Swirl by Swirl: Spirals in Nature (Author Joyce Sidman; Pictures by Beth Krommes) Houghton Mifflin, 2011, ISBN: 9780547315836