A note on Laguerre-type and Euler type Grandi's roses

Diego Caratelli; Primo Brandi; Paolo Emilio Ricci

doi:10.26830/symmetry_2025_1_083

A note on Laguerre-type and Euler type Grandi's roses

Diego Caratelli
, Primo Brandi
, Paolo Emilio Ricci (Corresponding author)

Electromagnetics

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Starting from the connection between the cartesian and the polar equation of a given curve, we introduce two different types of Grandi's roses (also called rhodoneas curves) with integer degree. The first extension is connected with the Laguerre-type exponentials, and the second one deals with the Euler's nearly cosine series. Several graphs of the relevant curves are shown, derived by the first author using the Mathematica^Ò computer algebra program.

Original language	English
Pages (from-to)	83-95
Number of pages	13
Journal	Symmetry: Culture and Science
Volume	36
Issue number	1
DOIs	https://doi.org/10.26830/symmetry_2025_1_083
Publication status	Published - 2025

Bibliographical note

Publisher Copyright:
© 2025, Symmetrion. All rights reserved.

Keywords

Euler's nearly cosine series
Grandi's roses
Laguerre-type exponentials
pseudo-Chebyshev functions
Spirals

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10.26830/symmetry_2025_1_083

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KW - pseudo-Chebyshev functions

KW - Spirals

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A note on Laguerre-type and Euler type Grandi's roses

Abstract

Bibliographical note

Keywords

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