Fibonacci数列与黄金分割数

Fibonacci Sequence and Golden Section Number

记{Fn}为Fibonacci数列.一个已知的事实是:比值数列{Fn/Fn+1}是收敛的,而且其极限恰为黄金分割数.文章给出这一基本结论的一个新的、内蕴的证明.同时,由此得到黄金分割数的连分数表达.

Let {Fn} be Fibonacci sequence. A well-known and important fact is that the ratio sequence {Fn/Fn＋1} is convergent and that the limit is just the golden section number. In this paper we give a new and intrinsic proof for this result. At the same time, we attain a continued fraction expression for the golden section number.