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Given a point $(p,q)$ with nonnegative integer coordinates and $p\not=q$, weprove 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 whoseendpoints are the B\'ezout coefficients of coprime numbers belonging toneighborhoods of $(p,q)$ and $(q,p)$, respectively.

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