Articles producció científica> Escola Tècnica Superior d'Arquitectura

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

  • Identification data

    Identifier: imarina:9285474
    Handle: http://hdl.handle.net/20.500.11797/imarina9285474
  • Authors:

    Herrera B
    Samper A
  • Others:

    Author, as appears in the article.: Herrera B; Samper A
    Department: Escola Tècnica Superior d'Arquitectura
    URV's Author/s: Herrera Gómez, Blas / Samper Sosa, Albert
    Keywords: Quasi-equivalent oval Quadrarc Geometría Ellipse Eight-centered oval
    Abstract: 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.
    Thematic Areas: Mathematics Geometry and topology Ensino Engenharias i Ciencias sociales Ciência da computação Arquitetura e urbanismo Applied psychology Applied mathematics
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: albert.samper@urv.cat blas.herrera@urv.cat
    Author identifier: 0000-0002-4795-2127 0000-0003-2924-9195
    Record's date: 2023-02-27
    Papper version: info:eu-repo/semantics/publishedVersion
    Licence document URL: http://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Journal For Geometry And Graphics. 19 (2): 257-268
    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
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2015
    Publication Type: Journal Publications
  • Keywords:

    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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