对数螺线、黄金分割与斐波那契数列的完美统一

The Perfect Unity of Logarithmic Spiral,Golden Section and Fibonacci Sequence

本文对对数螺线、黄金分割与斐波那契数列之间的关系进行研究,把线段上黄金分割点的定义推广到射线上的黄金分割点列,发现过极轴上任意一点有且仅有一条特殊的对数螺线与极轴的交点所成的点列为黄金分割点列,并把这个点列所对应的坐标定义为黄金分割数列,我们发现首项为115的黄金分割数列无限逼近于斐波那契数列。

In this paper, the relationship of the logarthmie spiral,golden section and Fibonacci sequence was studied, and the definition of golden section point of a segment was extended to golden section point hst of a ray. We found that there is only one special logarithmic spiral which passes through any given point on the polar axis, the intersections which the logarithmic spiral intersects with the polar axis constitute a golden section point list. The corresponding coordinate of the point list was defined as gold section sequence. We also found that the gold section sequence which first term is 1/√15infinitely approximate to the Fibonacci sequence.