From Chris Bartlett (Professor Emeritus of Art):

Dear friends and colleagues,

As many of you know, I retired in late summer 2015. Since then, my apotheosis, after over two years of intensive research and reviews, my paper, Nautilus Spirals and the Meta-Golden Ratio Chi was just published. 

What’s that got to do with art you may say? Well, the myth of the Golden ratio is one thing. Another is my discovery of the Chi mathematical constant while analyzing the geometry of Fairfield Porter’s painterly compositions.

Abstract

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.

Read full text: Nautilus Spirals and the Meta-Golden Ratio Chi