Dynamic construction of a family of octic curves as geometric loci-Reference-Cited by-同舟云学术

Dynamic construction of a family of octic curves as geometric loci

Published:2023 Issue:8 Volume:8 Page:19461-19476
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Dana-Picard Thierry¹,Recio Tomás²

Affiliation:

1. Department of Mathematics, Jerusalem College of Technology, Havaad Haleumi Street 21, Jerusalem 9116011, Israel

2. Universidad Antonio de Nebrija, C/Santa Cruz de Marcenado 27, 28015 Madrid, Spain

Abstract

<abstract><p>We explore the construction of curves of degree 8 (octics) appearing as geometric loci of points defined by moving points on an ellipse and its director circle. To achieve this goal we develop different computer algebra methods, dealing with trigonometric or with rational parametric representations, as well as through implicit polynomial equations, of the given curves. Finally, we highlight the involved mathematical or computational issues arising when reflecting on the outputs obtained in each case.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference20 articles.

1. M. Abanades, F. Botana, A. Montes, T. Recio, An algebraic taxonomy for locus computation in dynamic geometry, Comput. Aided Design, 56 (2014), 22–33. https://doi.org/10.1016/j.cad.2014.06.008

2. J. G. Alcazar, On the shape of rational algebraic curves depending on one parameter, Comput. Aided Geom. D., 27 (2009), 162–178. https://doi.org/10.1016/j.cagd.2009.11.004

3. J. G. Alcazar, J. Schicho, J. R. Sendra, A delineability-based method for Computing Critical Sets of Algebraic Surfaces, J. Symb. Comput., 42 (2007), 678–691. https://doi.org/10.1016/j.jsc.2007.02.001

4. D. Cox, J. Little, D. O'Shea, Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, Undergraduate Texts in Mathematics, NY: Springer, (1992).

5. Th. Dana-Picard, Automated study of a regular trifolium, Math. Comput. Sci., 13 (2018), 57–67.

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Inflexions of Spiric Curves: A Tale of Two Tori;Mathematics in Computer Science;2024-02-22

2. 3D Space Trajectories and beyond: Abstract Art Creation with 3D Printing;Electronic Proceedings in Theoretical Computer Science;2024-01-22