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斐波那契数列相邻两项之比我们把斐波那契数列改成纵向排列,并在左侧给出上下两个相邻数的比值,即依次列出1÷1=1,1÷2=0.5,2÷3≈0.666 667,……可以看出,随着项数的增加,这个比值正在逐渐逼近数0.618…,也就是逼近黄金分割数.这可以从它的通项F_n的结构得到解释此外,由黄金分割数x满足x=1/(1+x),反复把x代入即得所示的各级连分数,其值的分子、分母正好是相邻斐波那契数.
Fibonacci sequence of the ratio of the number of adjacent two We change the Fibonacci sequence into a vertical arrangement, and on the left gives the ratio of the upper and lower two adjacent numbers, which in turn lists 1 ÷ 1 = 1,1 ÷ 2 = 0.5,2 ÷ 3 ≈ 0.666 667, ... It can be seen that as the number of terms increases, the ratio is gradually approaching 0.618 ..., that is, approaching the golden number, which can be derived from its general structure of F_n In addition, the number of the golden section x satisfies x = 1 / (1 + x). Repeatedly inserting x into each successive fraction as shown, the numerator and denominator of the value are exactly adjacent Fibonacci numbers.