| 对数螺线、黄金分割与斐波那契数列的完美统一的 |
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| 引用本文： | 方海泉,周铁军,桑宝祥,李伟.对数螺线、黄金分割与斐波那契数列的完美统一的[J].数学理论与应用,2009(4):10-13. |
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| 作者姓名： | 方海泉 周铁军 桑宝祥 李伟 |
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| 作者单位： | 湖南农业大学理学院,长沙410128 |
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| 摘 要： | 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1/√15黄金分割数列无限逼近于斐波那契数列。
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| 关 键 词： | 对数螺线 黄金分割 斐波那契数列 黄金分割点列 |
The Perfect Unity of Logarithmic Spiral,Golden Section and Fibonacci Sequence |
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| Fang Haiquan Zhou Tiejun Sang Baoxing Li Wei.The Perfect Unity of Logarithmic Spiral,Golden Section and Fibonacci Sequence[J].Mathematical Theory and Applications,2009(4):10-13. |
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| Authors: | Fang Haiquan Zhou Tiejun Sang Baoxing Li Wei |
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| Institution: | Fang Haiquan Zhou Tiejun Sang Baoxing Li Wei (Science College of Hunan Agricultural University,Changsha,410028) |
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| Abstract: | In this paper,the relationship of the logarthmic spiral, golden section and Fibonacci sequence was studied,and the definition of golden sec tion point of a segment was extended to golden section point list of a ray.We fo und that there is only one special logarithmic spiral which passes through any g iven point on the polar axis,the intersections which the logarithmic spiral inte rsects with the polar axis constitute a golden section point list.The correspond ing coordinate of the point list was defined as ... |
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| Keywords: | Logarithmic spiral Golden sectioin Fibonacci sequence G olden section point list |
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