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Definition and calculation of an eight-centered oval which is quasi-equivalent to the ellipse

  • Dades identificatives

    Identificador: imarina:9285474
    Autors:
    Herrera BSamper A
    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.
  • Altres:

    Autor segons l'article: Herrera B; Samper A
    Departament: Escola Tècnica Superior d'Arquitectura
    Autor/s de la URV: Herrera Gómez, Blas / Samper Sosa, Albert
    Paraules clau: Quasi-equivalent oval Quadrarc Geometría Ellipse Eight-centered 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: Mathematics Geometry and topology Ensino Engenharias i Ciencias sociales Ciência da computação Arquitetura e urbanismo Applied psychology Applied mathematics
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: albert.samper@urv.cat blas.herrera@urv.cat
    Identificador de l'autor: 0000-0002-4795-2127 0000-0003-2924-9195
    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
  • Paraules clau:

    Applied Mathematics,Applied Psychology,Geometry and Topology,Mathematics
    Quasi-equivalent oval
    Quadrarc
    Geometría
    Ellipse
    Eight-centered oval
    Mathematics
    Geometry and topology
    Ensino
    Engenharias i
    Ciencias sociales
    Ciência da computação
    Arquitetura e urbanismo
    Applied psychology
    Applied mathematics
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