A Note on Spirals and Curvature
- https://doi.org/10.2991/gaf.k.200124.001How to use a DOI?
- Spirals; pseudo-Chebyshev functions; curvature; Lamé curves; Antonelli metrics
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.
- © 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 -