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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CITATION STYLE
Gielis, J., Caratelli, D., Moreno de Jong van Coevorden, C., & Ricci, P. E. (2018). The common descent of biological shape description and special functions. In Springer Proceedings in Mathematics and Statistics (Vol. 230, pp. 119–131). Springer New York LLC. https://doi.org/10.1007/978-3-319-75647-9_10
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