Arrangement of Sunflower Seeds and Efficient Packing
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Abstract
In this article, we propose ideas of pattern formation in nature and in laboratories, examples of quasipattern formation, relation between Fibonacci sequence and golden number, arrangement of sunflower seeds, and efficiency of arrangement of sunflower seeds. Under some conditions, such arrangement presents the dense packing of seeds and the least free space.
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บทความวิชาการ
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References
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[2] J. Ridley, “Packing efficiency in sunflower heads,” Mathematical Biosciences, vol.58. no.1, pp. 129–139, 1982.
[3] Blaze Labs. (2015, September 10). From waves to particles by standing waves in space. [Online]. Available: https://www.blazelabs. com/f−p−oscillon.asp
[4] A. Cook. (2015, November 11). Sand dunes and ripples in Death Valley National Park. [Online].Available: https://www.rockymtnrefl.com/DeathValleyRipplescd47322.html
[5] Bees and honeycomb 21462. (2014, November 20). Bees and honeycomb 21462. [Online]. Available: https://www.freegreatpicture.com/animal−collection/bees−and−honeycomb−21462
[6] C. Junell. (2007, July 16). Sunflower Spiral. [Online]. Available: https://commons.wikimedia.org/wiki/File :Sunflower_Spiral.jpg
[7] Fibonacci and Nature. (2015, November 21). Fibonacci and Nature. [Online]. Available: https://www.mur derous maths.co.uk/ books/BKMM8xgr.htm
[8] Liaisonwithalison. (2015, November 24) Fibonacci Sequence. [Online]. Available: https://liaisonwithalison.word press. com/2015/03/24/fibonacci−sequence/
[9] H. Vogel, “A better way to construct the sun flower head,” Mathematical Biosciences, vol. 44, no. 3–4, pp.179–189, June 1979.
[10] H. Segerman, “The sunflower spiral and the Fibonacci metric,” in Proceedings of Bridges 20 10: Mathematics, Music, Art, Architecture, Cul−ture, pp. 483–486, 2010.
[11] J. S. Hanan, F.D. Fracchia, D. Fowler, M. J. M. de Boer, and L. Mercer, The Algorithmic Beauty of Plants. New York : Springer−Verlag, 1990.
[12] J. D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications (Interdis ciplinary Applied Mathematics) (v.2), 3rd ed. USA: Springer−Verlag, 2002.