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Symmetry: Culture and Science
Volume 32, Number 2, pages 157-160 (2021)
https://doi.org/10.26830/symmetry_2021_2_157

THE APEIROGON AND DUAL NUMBERS

Johan Gielis1,*, Simone Brasili2

1 Department of Biosciences Engineering, University of Antwerp, Belgium
E-mail: johan.gielis@uantwerpen.be
ORCID: 0000-0002-4536-3839

2 Mathematics Division, School of Science and Technology, University of Camerino, Italy
E-mail: simone.brasili@unicam.it
ORCID: 0000-0002-4925-5237

* corresponding author

Abstract: The richness, diversity, connection, depth and pleasure of studying symmetry continue to open doors. Here we report a connection between Coxeter’s Apeirogon and the geometry associated with pictorial space, parabolic rotation and dual numbers.

Keywords: polygons, apeirogon, parabolic rotation, dual numbers, perception.
MSC 2020: 11G42

References:
Brasili, S., Piergallini, R. (2021) Symmetry and invariance: interdisciplinary teaching. In: Complex Symmetries. Ed. G. Darvas. World Scientific.

Coxeter, H.S.M. (1963) Regular Polytopes. 2nd ed., New York: Dover, 321 pp.

Coxeter, H.S.M. (1974) Regular Complex Polytopes. Cambridge: Cambridge University Press, 185 pp.

Gielis, J. (2017) The Geometrical Beauty of Plants. Atlantis/Springer, 254 pp. https://doi.org/10.2991/978-94-6239-151-2

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Koenderink, J., van Doorn, A. (2012) Gauge fields in pictorial space. SIAM Journal on Imaging Sciences, 5, 4, 1213-1233. https://doi:10.1137/120861151

Ricci, P.E. (2020) A note on the D-trigonometry and the relevant D-Fourier expansions. Growth and Form, 2, 1, 11-16. https://doi.org/10.2991/gaf.k.201210.002

Yaglom, I.M. (1979) A Simple Non-Euclidean Geometry and Its Physical Basis. Heidelberg Science Library, Springer, 307 pp.

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