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Journal Article

# Shape and Order in Organic Nature: The Nautilus Pompilius

Rory Fonseca
Leonardo
Vol. 26, No. 3 (1993), pp. 201-204
DOI: 10.2307/1575811
Stable URL: http://www.jstor.org/stable/1575811
Page Count: 4

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## Abstract

The Nautilus pompilius is an exquisite example of a planar logarithmic spiral in organic nature, yet many artists and designers claim that its shape is ordained by the Golden Section, symbolically represented by φ, where $\phi =(\sqrt{5}+1)/2=1.6180$ In a logarithmic spiral, shape is conventionally analyzed by examining the growth-ratios of radius vectors. These ratios are constant for a particular curve and form the basis for calculating the acute angle β between a tangent at any point on the curve and its polar radius vector--each spiral has a unique β. The magnitude of β controls the sweep of the curve, and the closer this angle β is to 90° the tighter the spiral. For the Nautilus pompilius illustrated in this paper, the average growth-ratio of radius vectors, for θ = 90°, is in the order of 1:1.3158, which yields a constant angle β of about 80°.

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