Israel Journal of Mathematics

, Volume 4, Issue 2, pp 65–82 | Cite as

Measures of axial symmetry for ovals

  • B. Abel Devalcourt


A measure of axial symmetry for ovals is defined, and eleven particular measures are studied. Lower bounds for these measures are determined on the classes of arbitrary ovals, centrally symmetric ovals, and ovals of constant breadth. The proofs of these results make use only of elementary geometry and the properties of convexity.


Axial Symmetry Isoperimetric Inequality Constant Breadth Load Curve Support Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. D. Chakerian and S. K. Stein,On measures of symmetry of convex bodies, Canad. J. Math.17 (1965), 497–504.MATHMathSciNetGoogle Scholar
  2. 2.
    B. A. deValcourt, A Study of Axial Symmetry of Planar Convex Sets (unpublished Ph.D. thesis, University of Minnesota, 1965).Google Scholar
  3. 3.
    B. A. deValcourt,Axially symmetric polygons inscribed in and circumscribed about convex sets (to appear in Elem. Math.).Google Scholar
  4. 4.
    B. Grünbaum,Measures of symmetry for convex sets, Proceedings of Symposia in Pure Mathematics. Vol. VII, Convexity. Amer. Math. Soc. Providence, R. I. 1963.Google Scholar
  5. 5.
    F. Krakowski,Bemerkung zu einer Arbeit von W. Nohl. Elem. Math.18 (1963), 60–61.MATHGoogle Scholar
  6. 6.
    W. Nohl,Die innere axiale Symmetrie zentrischer Eibereiche der euklidischen Ebene Elem. Math17 (1962), 59–63.MATHGoogle Scholar
  7. 7.
    J. Pàl,Uber ein elementares Variationsproblem, Math.-phys. Medd., Danske Vid. Selsk.3 (1920).Google Scholar
  8. 8.
    K. Zindler,Über konvexe Gebilde, I, II, III, Monatsh. Math. Phys.30 (1920) 87–102;31 (1921), 25–56;32 (1922), 107–138.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1966

Authors and Affiliations

  • B. Abel Devalcourt
    • 1
  1. 1.College of Santa FeSanta Fe

Personalised recommendations