某些植物中叶片的美丽排列，称为叶序，遵循一些微妙的数学关系。 例如，向日葵花盘中的小花形成两个方向相反的螺旋：55 个顺时针方向和 34 个逆时针方向。 令人惊讶的是，这些数字是连续的 斐波那契数。 间隔 斐波那契数 的比率由收敛值 
给出，其中 
是 黄金比例，据说衡量植物茎上连续叶片之间转动的分数：榆树和椴树为 1/2，山毛榉和榛树为 1/3，橡树和苹果树为 2/5，杨树和玫瑰为 3/8，柳树和杏树为 5/13 等。（Coxeter 1969，Ball 和 Coxeter 1987）。 类似的现象也发生在雏菊、菠萝、松果、花椰菜等等。
百合花、鸢尾花和延龄草有三片花瓣； 耧斗菜、毛茛花、翠雀花和野玫瑰有五片花瓣； 飞燕草、血根草和波斯菊有八片花瓣； 玉米万寿菊有 13 片花瓣； 紫菀有 21 片花瓣； 雏菊有 34、55 或 89 片花瓣——全部都是 斐波那契数。
另请参阅
Daisy,
Fibonacci Number,
Golden Angle,
Spiral
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参考文献
Azukawa, K. and Yuzawa, T. "A Remark on the Continued Fraction Expansion of Conjugates of the Golden Section." Math. J. Toyama Univ. 13, 165-176, 1990.Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 第 13 版 New York: Dover, pp. 56-57, 1987.Church, A. H. The Relation of Phyllotaxis to Mechanical Laws. London: Williams and Norgate, 1904.Church, A. H. On the Interpretation of Phenomena of Phyllotaxis. Riverside, NJ: Hafner, 1968.Conway, J. H. and Guy, R. K. "Phyllotaxis." In The Book of Numbers. New York: Springer-Verlag, pp. 113-125, 1995.Cook, T. A. The Curves of Life, Being an Account of Spiral Formations and Their Application to Growth in Nature, To Science and to Art. New York: Dover, 1979.Coxeter, H. S. M. "The Golden Section and Phyllotaxis." Ch. 11 in Introduction to Geometry, 2nd ed. New York: Wiley, 1969.Coxeter, H. S. M. "The Role of Intermediate Convergents in Tait's Explanation for Phyllotaxis." J. Algebra 10, 167-175, 1972.Coxeter, H. S. M. "The Golden Section, Phyllotaxis, and Wythoff's Game." Scripta Mathematica 19, 135-143, 1953.Dixon, R. "The Mathematics and Computer Graphics of Spirals in Plants." Leonardo 16, 86-90, 1983.Dixon, R. Mathographics. New York: Dover, 1991.Douady, S. and Couder, Y. "Phyllotaxis as a Self-Organized Growth Process." In Growth Patterns in Physical Sciences and Biology (Ed. J. M. Garcia-Ruiz et al. ). New York: Plenum, 1993.Gardner, M. Mathematical Circus: More Puzzles, Games, Paradoxes and Other Mathematical Entertainments from Scientific American. New York: Knopf, 1979.Hargittai, I. and Pickover, C. A. (编辑). Spiral Symmetry. New York: World Scientific, 1992.Hunter, J. A. H. and Madachy, J. S. Mathematical Diversions. New York: Dover, pp. 20-22, 1975.Jean, R. V. "Number-Theoretic Properties of Two-Dimensional Lattices." J. Number Th. 29, 206-223, 1988.Jean, R. V. "On the Origins of Spiral Symmetry in Plants." In Spiral Symmetry. (Ed. I. Hargittai and C. A. Pickover). New York: World Scientific, pp. 323-351, 1992.Jean, R. V. Phyllotaxis: A Systematic Study in Plant Morphogenesis. New York: Cambridge University Press, 1994.Naylor, M. "Golden, 
, and 
Flowers: A Spiral Story." Math. Mag. 75, 163-172, 2002.Livio, M. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway Books, 2002.Pappas, T. "The Fibonacci Sequence & Nature." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 222-225, 1989.Prusinkiewicz, P. and Lindenmayer, A. The Algorithmic Beauty of Plants. New York: Springer-Verlag, 1990.Steinhaus, H. Mathematical Snapshots, 第 3 版 New York: Dover, p. 138, 1999.Stevens, P. S. Patterns in Nature. London: Peregrine, 1977.Stewart, I. "Daisy, Daisy, Give Me Your Answer, Do." Sci. Amer. 200, 96-99, Jan. 1995.Thompson, D. W. On Growth and Form. Cambridge, England: Cambridge University Press, 1952.Trott, M. Graphica 1: The World of Mathematica Graphics. The Imaginary Made Real: The Images of Michael Trott. Champaign, IL: Wolfram Media, pp. 11 and 83, 1999.Vogel, H. "A Better Way to Construct the Sunflower Head." Math. Biosci. 44, 179-189, 1979.Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, pp. 65-66, 1986.在 中引用
叶序
引用为
Weisstein, Eric W. “叶序。” 来自 —— 资源。 https://mathworld.net.cn/Phyllotaxis.html
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