Bézout Coefficients of Coprime Numbers Approximate Quadratic Bézier Curves

Given a point with nonnegative integer coordinates and , we prove that the quadratic Bézier curve relative to the points , , and is approximately the envelope of a family of segments whose endpoints are the Bézout coefficients of coprime numbers belonging to neighborhoods of and , respectively.

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Bibliographische Detailangaben
Veröffentlicht in:	Lobachevskii journal of mathematics 2023-07, Vol.44 (7), p.2838-2844
Hauptverfasser:	Itzá-Ortiz, Benjamín A., López-Hernández, Roberto, Miramontes, Pedro
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Analysis Curves Geometry Mathematical Logic and Foundations Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Given a point with nonnegative integer coordinates and , we prove that the quadratic Bézier curve relative to the points , , and is approximately the envelope of a family of segments whose endpoints are the Bézout coefficients of coprime numbers belonging to neighborhoods of and , respectively.
ISSN:	1995-0802 1818-9962
DOI:	10.1134/S1995080223070326