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Research Article | Open Access

Dynamic construction of a family of octic curves as geometric loci

Thierry Dana-Picard1( ), Tomás Recio2
Department of Mathematics, Jerusalem College of Technology, Havaad Haleumi Street 21, Jerusalem 9116011, Israel
Universidad Antonio de Nebrija, C/Santa Cruz de Marcenado 27, 28015 Madrid, Spain
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Abstract

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.

Keywords

plane curvesgeometric locusoctic curveinteractive constructiondynamic geometryGeoGebrasymbolic computationMapleimplicitization
CLC number: 14H50, 51M15, 13P10

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AIMS Mathematics
Volume 8 Issue 8,
August 2023
Pages 19461-19476
DOI: 10.3934/math.2023993

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Cite this article:
Dana-Picard T, Recio T. Dynamic construction of a family of octic curves as geometric loci. AIMS Mathematics, 2023, 8(8): 19461-19476. https://doi.org/10.3934/math.2023993

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Received: 29 March 2023
Revised: 17 May 2023
Accepted: 18 May 2023
Published: 15 August 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)