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Volume 33, Number 3, pages 201-208 (2022)
https://doi.org/10.26830/symmetry_2022_3_201
A META-DIVINE (ALLO)NAUTILUS
Dirk Huylebrouck*
* Department of Architecture, KU Leuven University, Belgium.
Email: dirk.huylebrouck@kuleuven.be
Web: http://www.dirkhuylebrouck.be
ORCID: 0000-0003-2760-1415
Abstract: Circular arcs inscribed in squares whose sides are Fibonacci numbers will never approach the shape of a Nautilus shell, and yet prominent authors mention this as fact. There is no connection with the golden ratio 1.618... and perhaps neither with 1.333..., as others subsequently proposed. So, what is the real ratio of the Nautilus shell?
Keywords: (Allo)Nautilus, Fibonacci spiral, Golden section myth, Meta-divine chi ratio.
References:
Bartlett, Ch. (2018) Nautilus spirals and the meta-golden ratio Chi, Nexus Network Journal, December. https://doi.org/10.1007/s00004-018-0419-3
Bartlett, C. and D. Huylebrouck (2013) Art and math of the 1.35 ratio rectangle, Symmetry: Culture and Science, 24, 1-4, 451-462. https://doi.org/10.26830/symmetry_2013_1-4_451
Falbo, C. (2005) The golden ratio: A contrary viewpoint, College Mathematics Journal, 36, 2, 123-134. https://doi.org/10.1080/07468342.2005.11922119
Huylebrouck, D. (2014) The meta-golden ratio Chi, Proceedings Bridges Seoul, 151-158.
Redondo Buitrago, A. (2013) On the ratio 1.3 and related numbers, Proceedings of 9th ISIS Congress, Panormo, Crete, Greece, Symmetry: Art and Science, 76-81.
Swinton, J., Ochu, E. (2016) The MSI Turing's sunflower consortium and Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment, Royal Society Open Science, 3, 5, 160091. https://doi.org/10.1098/rsos.160091
Trott, M., (2017) From aspect ratios in art: What is better than being golden? Being plastic, rooted, or just rational? Investigating aspect ratios of old vs. modern paintings, Blog.wolfram.com. (Accessed 8.12.17)
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