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arXiv · 2012.11770

B\'ezout coefficients of coprime numbers approximate quadratic B\'ezier curves

Benjamín A. Itzá-Ortiz·Roberto López Hernández·Pedro Miramontes
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Abstract

Given a point $(p,q)$ with nonnegative integer coordinates and $p\not=q$, we prove that the quadratic B\'ezier 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 B\'ezout coefficients of coprime numbers belonging to neighborhoods of $(p,q)$ and $(q,p)$, respectively.

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Benjamín A. Itzá-Ortiz, Roberto López Hernández, Pedro Miramontes. 2020-12-22. B\'ezout coefficients of coprime numbers approximate quadratic B\'ezier curves. https://doi.org/10.1134/s1995080223070326

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