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

  • Datos identificativos

    Identificador: imarina:9285474
    Autores:
    Herrera BSamper A
    Resumen:
    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.
  • Otros:

    Autor según el artículo: Herrera B; Samper A
    Departamento: Escola Tècnica Superior d'Arquitectura Enginyeria Informàtica i Matemàtiques
    Autor/es de la URV: Herrera Gómez, Blas / Samper Sosa, Albert
    Palabras clave: Eight-centered oval Ellipse Geometría Quadrarc Quasi-equivalent oval
    Resumen: 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.
    Áreas temáticas: Applied mathematics Applied psychology Arquitetura e urbanismo Ciência da computação Ciencias sociales Engenharias i Ensino Geometry and topology Mathematics
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    Direcció de correo del autor: blas.herrera@urv.cat albert.samper@urv.cat
    Identificador del autor: 0000-0003-2924-9195 0000-0002-4795-2127
    Fecha de alta del registro: 2023-02-27
    Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
    Referencia al articulo segun fuente origial: Journal For Geometry And Graphics. 19 (2): 257-268
    Referencia 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 Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2015
    Tipo de publicación: Journal Publications
  • Palabras clave:

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