Nautilus Spirals and the Meta-Golden Ratio Chi
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The Nautilus shell is the popular iconic image for a logarithmic spiral. It is also frequently cited as an example of a golden ratio logarithmic spiral in nature. Evidently, this not the case. Contrarian studies have proposed that the Nautilus spiral is actually in the 4:3 ratio. Yet, these recommendations are based on one, or just a few shells. In this research, to compare the mean aspect ratio of Nautilus shells to the 4:3 ratio and the meta-golden ratio Chi, eighty Nautilus shells were measured in the Smithsonian collection. The results show that the Nautilus genus is clearly not the widely quoted 4:3 (1.333), but averaged 1.310. However, there was one species that was remarkably different, the Crusty Nautilus averaging 1.356 which is an excellent match for the Meta-golden ratio Chi.
KeywordsMeta-golden Ratio Chi Nautilus spiral Logarithmic spirals Golden ratio spiral Myth Proportion Diagonals Geometry
I wish to thank the following: Dr. Mike Veccione and staff at NMNH; Dr. Neil Landman and staff at AMNH; Dr. René Hoffmann, Ruhr-University Bochum; Dr. Amane Tajika; Dr. Greg Barord; Christina Piotrowski, CAS; Prof. Yunwei Cui for statistical analyses; and Ms. Robin Williams for her unwavering support.
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