Growth and Form

Volume 1, Issue 1, 2020, Pages 1 - 8

A Note on Spirals and Curvature

Authors
Johan Gielis1, *, Diego Caratelli2, Peijian Shi3, Paolo Emilio Ricci4
1Department of Biosciences Engineering, University of Antwerp, Belgium
2The Antenna Company International, High Tech Campus, Eindhoven, The Netherlands
3Co-Innovation Centre for Sustainable Forestry in Southern China, Nanjing Forestry University, Jiangsu, People’s Republic of China
4Department of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II, Rome, Italy
*Corresponding author. Email: johan.gielis@uantwerpen.be
Corresponding Author
Johan Gielis
Received 1 September 2019, Accepted 18 October 2019, Available Online 23 February 2020.
DOI
https://doi.org/10.2991/gaf.k.200124.001How to use a DOI?
Keywords
Spirals; pseudo-Chebyshev functions; curvature; Lamé curves; Antonelli metrics
Abstract

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.

Copyright
© 2020 The Authors. Published by Atlantis Press SARL
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Growth and Form
Volume-Issue
1 - 1
Pages
1 - 8
Publication Date
2020/02/23
ISSN (Online)
2589-8426
DOI
https://doi.org/10.2991/gaf.k.200124.001How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press SARL
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Johan Gielis
AU  - Diego Caratelli
AU  - Peijian Shi
AU  - Paolo Emilio Ricci
PY  - 2020
DA  - 2020/02/23
TI  - A Note on Spirals and Curvature
JO  - Growth and Form
SP  - 1
EP  - 8
VL  - 1
IS  - 1
SN  - 2589-8426
UR  - https://doi.org/10.2991/gaf.k.200124.001
DO  - https://doi.org/10.2991/gaf.k.200124.001
ID  - Gielis2020
ER  -