Autor segons l'article: Herrera B; Samper A
Departament: Escola Tècnica Superior d'Arquitectura Enginyeria Informàtica i Matemàtiques
Autor/s de la URV: Herrera Gómez, Blas / Samper Sosa, Albert
Paraules clau: Eight-centered oval Ellipse Geometría Quadrarc Quasi-equivalent oval
Resum: Let ?b be an ellipse (b=minor axis/major axis). In this paper we consider different approximations by ovals, which are composed from circular arcs and have also two axes of symmetry. We study a) three four-centered ovals (quadrarcs) Oa4,bOc4,b, and Ol4,b, which share the vertices with the ellipse ?b. In addition, Oa4,b has the same surface area, Oc4,b has the minimum error of curvature at the vertices, and Ol4,b has the same perimeter length. b) Further, we investigate three eight-centered ovals Oc8,b, Oc-a8,b and Oc-l8,b which also share the vertices with ?b. The ovals Oc8,b have the same curvature at the vertices, and in addition, Oc-a8,b has the same surface area, and Oc-l8,b has the same perimeter length as ?b. As a conclusion, the eight-centered oval Oc-l8,b seems to be optimal and can therefore be called 'quasi-equivalent' to ?b. We show that the difference of surface areas Ab = A(Oc-l8,b)-A(?b) is rather small; the maximum value A0.1969 = 0.007085 is achieved at b = 0.1969. The deformation error Eb = E(?b, Oc-l8,b) has the maximum value 0.008970 which is achieved at b = 0.2379. © 2015 Heldermann Verlag.
Àrees temàtiques: Applied mathematics Applied psychology Arquitetura e urbanismo Ciência da computação Ciencias sociales Engenharias i Ensino Geometry and topology Mathematics
Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
Adreça de correu electrònic de l'autor: blas.herrera@urv.cat albert.samper@urv.cat
Identificador de l'autor: 0000-0003-2924-9195 0000-0002-4795-2127
Data d'alta del registre: 2023-02-27
Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
Referència a l'article segons font original: Journal For Geometry And Graphics. 19 (2): 257-268
Referència de l'ítem segons les normes APA: Herrera B; Samper A (2015). Definition and calculation of an eight-centered oval which is quasi-equivalent to the ellipse. Journal For Geometry And Graphics, 19(2), 257-268
URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
Entitat: Universitat Rovira i Virgili
Any de publicació de la revista: 2015
Tipus de publicació: Journal Publications
Repositori URV