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Bézout Coefficients of Coprime Numbers Approximate Quadratic Bézier Curves

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Abstract

Given a point \((p,q)\) with nonnegative integer coordinates and \(p\not=q\), we prove that the quadratic Bézier curve relative to the points \((p,q)\), \((0,0)\), and \((q,p)\) is approximately the envelope of a family of segments whose endpoints are the Bézout coefficients of coprime numbers belonging to neighborhoods of \((p,q)\) and \((q,p)\), respectively.

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Authors and Affiliations

  1. Centro de Investigación en Matemáticas, Universidad Autónoma del Estado de Hidalgo, Pachuca, Hidalgo, Mexico

    Benjamín A. Itzá-Ortiz & Roberto López-Hernández

  2. Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico, Mexico

    Pedro Miramontes

Authors
  1. Benjamín A. Itzá-Ortiz
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  2. Roberto López-Hernández
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  3. Pedro Miramontes
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Corresponding authors

Correspondence to Benjamín A. Itzá-Ortiz, Roberto López-Hernández or Pedro Miramontes.

Additional information

(Submitted by M. A.Malakhaltsev)

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Itzá-Ortiz, B.A., López-Hernández, R. & Miramontes, P. Bézout Coefficients of Coprime Numbers Approximate Quadratic Bézier Curves. Lobachevskii J Math 44, 2838–2844 (2023). https://doi.org/10.1134/S1995080223070326

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  • DOI: https://doi.org/10.1134/S1995080223070326

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