Growth and Form

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8 articles
Research Article

A Note on Spirals and Curvature

Johan Gielis, Diego Caratelli, Peijian Shi, Paolo Emilio Ricci
Pages: 1 - 8
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...
Research Article

The Möbius Phenomenon in Generalized Möbius-Listing Bodies with Cross Sections of Odd and Even Polygons

J. Gielis, I. Tavkhelidze
Pages: 1 - 10
In the study of cutting Generalized Möbius-Listing bodies with polygons as cross section, it is well known that the Möbius phenomenon, whereby the cutting process yields only one body, occurs only in even polygons with an even number of vertices and sides, and only in the specific when the knife cuts...
Research Article

Curvature Against the Grain

Jan Koenderink
Pages: 9 - 19
In mathematics “curvature” is described in various ways, but perhaps the most common is as a rate of spatial attitude. Such a definition is similar to the deviation from flatness, where flatness might again be understood (in various ways) in terms of congruence. In classical physics the notion of curvature...
Research Article

A Note on the D-trigonometry and the Relevant D-Fourier Expansions

Paolo Emilio Ricci
Pages: 11 - 16
Considering the diamond, i.e. the square inclined at an angle of 45°, it is possible to define the analogues of circular functions and to construct formulas that translate the trigonometric ones. The relative D-trigonometric functions have geometric shapes closely related to the corresponding classical...
Review Article

Chebyshev Polynomials, Rhodonea Curves and Pseudo-Chebyshev Functions. A Survey

Paolo Emilio Ricci
Pages: 20 - 32
In recent works, starting from the complex Bernoulli spiral and the Grandi roses, sets of irrational functions have been introduced and studied that extend to the fractional degree the polynomials of Chebyshev of the first, second, third and fourth kind. The functions thus obtained are therefore called...
Research Article

Classification of Planar Anisotropic Elasticae

Bennett Palmer, Álvaro Pámpano
Pages: 33 - 40
We classify the anisotropic elastic curves modulo rescaling and quasi-rotation depending on one parameter for an ample family of anisotropic functionals. Several illustrations of this classification are shown at the end.
Mini Review

Allometric Laws in Modular Dynamics: The Bauplan of Ontogenesis

Peter L. Antonelli, Solange F. Rutz
Pages: 41 - 43
In recent decades, a resurgence of allometry in ecology and its associated scaling laws has been observed, going under the name macroecology. It is reasonable to think that the plethora of current works on experimental physiology using allometry is a continuation of the tradition of searching for the...


Johan Gielis, Wendy Goemans
Pages: 44 - 45