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2018 | OriginalPaper | Buchkapitel

The Common Descent of Biological Shape Description and Special Functions

verfasst von : J. Gielis, D. Caratelli, C. Moreno de Jong van Coevorden, P. E. Ricci

Erschienen in: Differential and Difference Equations with Applications

Verlag: Springer International Publishing

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Abstract

Gielis transformations, with their origin in botany, are used to define square waves and trigonometric functions of higher order. They are rewritten in terms of Chebyshev polynomials. The origin of both, a uniform descriptor and the origin of orthogonal polynomials, can be traced back to a letter of Guido Grandi to Leibniz in 1713 on the mathematical description of the shape of flowers. In this way geometrical description and analytical tools are seamlessly combined.

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Metadaten
Titel
The Common Descent of Biological Shape Description and Special Functions
verfasst von
J. Gielis
D. Caratelli
C. Moreno de Jong van Coevorden
P. E. Ricci
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-75647-9_10