On Divisibility and ?- Periodicity in the Quasigeometric Fibonacci Sequence
Keywords:
γ-periodicity, Fibonacci sequence, golden section quasigeometric sequence, quasigeometric Fibonacci sequenceAbstract
The quasigeometric Fibonacci sequence has interesting divisibility properties, namely that and are integers. Results of this research show that and where and are golden section quasigeometric sequences. This phenomenon of periodicity is herein named periodicity. Concept is important in profiling the behavior of and the golden section and may be invoked in science and technology development.
References
. Elliot MA, Kelly J, Friedel J, Brodsky J, Mulcahy P. The golden section as optical limitation.PloS ONE. 2015;10(7):1-15.
. Navon D. The sisters of the golden section. Perception. 2011;40:705-24.
. Thapa GB, Thapa R. The relation of golden ratio, mathematics and aesthetics. Journal of the Institute of Engineering. 2018;14(1):188-99.
. Phillips ME. Rethinking the role of the golden section in music and music scholarship. Creativity Research Journal. 2019;31(4):419-27.
. Wares A. The golden ratio and regular hexagons. International Journal of Mathematical Education in Science and Technology. 2020;51(1):157-60.
. Widrick RM, Raskin JD. Age-related stigma and the golden section hypothesis. Aging and Mental Health. 2010;14(4):375-85.
. Raskin JD, Brett BL. Does the reverse golden section hold? Journal of Constructivist Psychology. 2014;27(2):137-46.
. Nikolic ST, CosicI, Pecujlija M, Miletic A. The effect of the ‘golden ratio’ on consumer behaviour. African Journal of Business Management. 2011;5(20):8347-60.
. Saraf S, Saraf P. The golden proportion: key to the secret of beauty. The Internet Journal of Plastic Surgery. 2013;9(1):1-16.
. Mamombe L. Proportiones perfectus law and the physics of the golden section. Asian Research Journal of Mathematics. 2017;7(1):1-41.
. Mamombe L. Golden section and evolving systems. Journal of Scientific Research and Reports. 2019;22(6):1-8.
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