A Visual Overview of Coprime Numbers

Benjamín A. Itzá-Ortiz (), Roberto López-Hernández () and Pedro Miramontes ()
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Benjamín A. Itzá-Ortiz: Universidad Autónoma del Estado de Hidalgo
Roberto López-Hernández: Universidad Autónoma del Estado de Hidalgo
Pedro Miramontes: Universidad Nacional Autónoma de México

Chapter 7 in Handbook of the Mathematics of the Arts and Sciences, 2021, pp 149-167 from Springer

Abstract: Abstract Some examples of geometric constructions based on prime numbers are presented. After that, a novel visualization of coprime numbers in the Cartesian plane based on Bézout coefficients is introduced. Using the classification of skew Sturmian sequences as a departing point, it becomes natural to select certain subsets of coprime numbers which contain the dynamical information of skew Sturmian sequences up to conjugacy. When plotting these sets, astonishing geometric structures emerge. Among them are some parabolic arcs; their parametric representations are given.

Keywords: Coprime numbers; Bézout coefficients; Skew Sturmian sequence; Quadratic arc (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-57072-3_139

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DOI: 10.1007/978-3-319-57072-3_139

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