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Title
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A note on spirals and curvature
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Author
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Abstract
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| Starting from logarithmic, sinusoidal and power spirals, it is shown how these spirals are connected directly with Chebyshev polynomials, Lamé curves, with allometry and Antonelli-metrics in Finsler geometry. Curvature is a crucial concept in geometry both for closed curves and equiangular spirals, and allowed Dillen to give a general definition of spirals. Many natural shapes can be described as a combination of one of two basic shapes in nature—circle and spiral—with Gielis transformations. Using this idea, shape description itself is used to develop a novel approach to anisotropic curvature in nature. Various examples are discussed, including fusion in flowers and its connection to the recently described pseudo-Chebyshev functions. |
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Language
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English
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Source (journal)
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Growth and form
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Publication
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2020
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DOI
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10.2991/GAF.K.200124.001
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Volume/pages
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1
:1
(2020)
, p. 1-8
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Full text (Publisher's DOI)
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Full text (open access)
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