中文题名: | Fibonacci数列的性质及推广以及植物中的Fibonacci数列 |
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保密级别: | 公开 |
论文语种: | chi |
学科代码: | 070101 |
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学生类型: | 学士 |
学位: | 理学学士 |
学位年度: | 2007 |
学校: | 北京师范大学 |
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第一导师姓名: | |
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提交日期: | 2007-06-30 |
答辩日期: | 2007-06-01 |
外文题名: | The properties and expansions of Fibonacci series and Fibonacci series in the plants |
中文关键词: | Fibonacci数列 ; 黄金分割 ; 行列式 ; lucas数列 ; 植物叶序 |
外文关键词: | Fibonacci series ; the golden section ; determinant ; Lucas series ; phyllotaxis of plants |
中文摘要: |
Fibonacci 数列是历史上最有名的数列之一,它是由意大利数学家Fibonacci在他的《算盘书》(Liber Abbaci)中提出来的。它在人口理论、对策论、最优化理论、层次分析、运筹学领域都有十分广泛的应用。本文首先就Fibonacci 数列的由来、计算和性质做了详细叙述,然后介绍了Fibonacci数列的两个推广:Fibonacci 数列的通项与行列式的关系,以及广义 Fibonacci 数列。最后将Fibonacci 数列与植物里面一些现象联系到一起以及加以分析:Fibonacci 数列与植物花瓣及植物叶序的关系,并分析了植物中存在Fibonacci 数的理由。 |
外文摘要: |
Fibonacci series is one of the most well-known series in the history, proposed by Italian mathematician Fibonacci, in his book . It has a very wide range of applications in many fields, such as Population Theory, Game Theory, Optimization Theory, Analytic Hierarchy Process, and Operation Research. This paper first gave a detailed description of the origin, calculation and properties of Fibonacci series, and then intro-duced its two expansions: relationship between general term of Fibo-nacci series and the determinant, and generalized Fibonacci series. At last, we linked together and analyzed the Fibonacci series and some phe- nomena of plants such as: the connection of Fibonacci series and plant petals and the phyllotaxis plants, and we analyzed the reason why Fibonacci series exist in such plants phenomena. |
参考文献总数: | 9 |
馆藏号: | 本070101/07019 |
开放日期: | 2024-03-14 |