Fibonacci sequence and biological sciences

Document Type : Review Paper

Authors

1 Department of Mathematics, Payam Noor University, Tehran, Iran

2 Department of Biology, Payam Noor University, Tehran, Iran

Abstract

 In this article we try to remind the reader that no knowledge is possible without mathematics. Mathematics is the science of thought and the basis of human thought and it is about finding, describing and understanding the order that lies in seemingly complex and chaotic situations. Abstract mathematical theories are directly related to nature and can be used to interpret it. In this regard, Norbert Wiener has a beautiful saying: “It seems that one can sit from the morning to evening watching the cute and strange creams of water but in the midst of all this beauty, I was drawn to mathematics and physics and those mathematical laws, which govern all these disordered masses of water” [18]. In this paper, with a review of fractal geometry, the Fibonacci sequence, symmetry, we describe their application in the regular biological sciences which lies in the seemingly complex situations of biology.

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[1] A. Chang and T. Zhang, The fractal geometry of the boundary of the dragon curves, J. Recreat. Math. 30 (2000) 9-22.
[2] A. J. Crilly, R. A. Earnshaw and H. Jones, Fractals and Chaos, Springer-Verlag. 1991. NewYork, USA.
[3] M. Golubitsky and L. Stewart, Symmetry methods in mathematical biology, Sao Paulo J. Math. Sci. 9 (2015) 1-36.
[4] A. Gupta, G. S. Rash, N. N. Somia, M. P. Wachowiak, J. Jones and A. Desoky, The motion path of the digits, J. Hand Surg. 23 (1998) 1038-1042.
[5] R. Hamilton and R. A. Dunsmuir, Radiographic assessment of the relative lengths of the bones of the fingers of the human hand, J. Hand Surg. Br. 27 (2002) 546-548.
[6] E. Levin, Dental esthetics and the golden proportion, J Prosthet Dent. 40 (1978) 244-252.
[7] J. W. Littler, On the adaptability of man’s hand (with reference to the equiangularcurve), Hand. 5 (1973) 187-191.
[8] R. E. Lombardi, The principles of visual perception and their clinical applicationto denture esthetics, J. Prosthet. Dent. 29 (1973) 358-382.
[9] J. C. Perez, Codon populations in single-stranded whole human genome DNA are fractal and fine-tuned by the Golden Ratio 1.618, Inter-discip. Sci. 2 (2010) 228-240.
[10] J. C. Perez, Chaos DNA and Neuro-computers: A golden link: The hidden language of genes, global language and order in the human genome, Speculations Sci. Technol. 14 (1991) 336-346.
[11] D. Persaud and J. P. O’Leary, Fibonacci Series, Golden Proportions, and the Human Biology, Austin J. Surg. (5)(2) (2015).
[12] R. M. Ricketts, The biologic significance of the divine proportion and Fibonacci series, Am. J. Orthod. 81 (1982) 351-370.
[13] N. Rivier, R. Occelli, J. pantaloni and A. Lissowski, Structure of benard convection cells, phyllotaxis and crystallography in cylindrical symmetry, J. physique .45 (1984) 49-63.
[14] M. E. Yamagishi and A. I. Shimabukuro, Nucleotide frequencies in human genomeand fibonacci numbers, Bull. Math. Biol. 70 (2008) 643-653.
[15] G. Yetkin, N. Sivri, K. Yalta and E. Yetkin, Golden Ratio is beating in our heart, Int. J. Cardiol. 168 (2013) 4926-4927.
[16] مانی رضایی، هندسه فرکتال، مجله ریاضی دانشجویان دانشگاه صنعتی شریف، شماره سوم، (1370).
[17] پرویز شهریاری، من ریاضیدانم، چاپخانه صنوبر، 1364.
[18] ابولقاسم لاله، گروه ها و تقارن. نشر دانش امروز (وابسته به موسسه انتشارات امیرکبیر)، 1371.
[19] منصور معتمدی، نسبت طلایی و اعداد فیبوناتچی، انتشارات خانه ریاضیات اصفهان، 1385.