Geodesic
Rational Bézier curves with infinitely many integral points
Archivum mathematicum, Tome 59 (2023) no. 4, pp. 339-349.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper we consider rational Bézier curves with control points having rational coordinates and rational weights, and we give necessary and sufficient conditions for such a curve to have infinitely many points with integer coefficients. Furthermore, we give algorithms for the construction of these curves and the computation of theirs points with integer coefficients.
DOI : 10.5817/AM2023-4-339
Classification : 14H25, 14H45, 14H50, 14Q05, 65D17
Keywords: Bézier curve; rational Bézier curve; curve of genus 0; integral point 
@article{10_5817_AM2023_4_339,
     author = {Dospra, Petroula},
     title = {Rational {B\'ezier} curves with infinitely many integral points},
     journal = {Archivum mathematicum},
     pages = {339--349},
     publisher = {mathdoc},
     volume = {59},
     number = {4},
     year = {2023},
     doi = {10.5817/AM2023-4-339},
     mrnumber = {4641950},
     zbl = {07790551},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2023-4-339/}
}
TY  - JOUR
AU  - Dospra, Petroula
TI  - Rational Bézier curves with infinitely many integral points
JO  - Archivum mathematicum
PY  - 2023
SP  - 339
EP  - 349
VL  - 59
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2023-4-339/
DO  - 10.5817/AM2023-4-339
LA  - en
ID  - 10_5817_AM2023_4_339
ER  - 
%0 Journal Article
%A Dospra, Petroula
%T Rational Bézier curves with infinitely many integral points
%J Archivum mathematicum
%D 2023
%P 339-349
%V 59
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2023-4-339/
%R 10.5817/AM2023-4-339
%G en
%F 10_5817_AM2023_4_339
Dospra, Petroula. Rational Bézier curves with infinitely many integral points. Archivum mathematicum, Tome 59 (2023) no. 4, pp. 339-349. doi : 10.5817/AM2023-4-339. http://geodesic.mathdoc.fr/articles/10.5817/AM2023-4-339/

Cité par Sources :