Hedgehogs of constant width and equichordal points

Yves Martinez-Maure

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 3, page 285-288
  • ISSN: 0066-2216

Abstract

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We give a characterization of convex hypersurfaces with an equichordal point in terms of hedgehogs of constant width.

How to cite

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Yves Martinez-Maure. "Hedgehogs of constant width and equichordal points." Annales Polonici Mathematici 67.3 (1997): 285-288. <http://eudml.org/doc/270415>.

@article{YvesMartinez1997,
abstract = {We give a characterization of convex hypersurfaces with an equichordal point in terms of hedgehogs of constant width.},
author = {Yves Martinez-Maure},
journal = {Annales Polonici Mathematici},
keywords = {convex body; hypersurface; pedal; equichordal; hedgehog; equichordal point; constant width},
language = {eng},
number = {3},
pages = {285-288},
title = {Hedgehogs of constant width and equichordal points},
url = {http://eudml.org/doc/270415},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Yves Martinez-Maure
TI - Hedgehogs of constant width and equichordal points
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 3
SP - 285
EP - 288
AB - We give a characterization of convex hypersurfaces with an equichordal point in terms of hedgehogs of constant width.
LA - eng
KW - convex body; hypersurface; pedal; equichordal; hedgehog; equichordal point; constant width
UR - http://eudml.org/doc/270415
ER -

References

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  2. [2] M. Fujiwara, Über die Mittelkurve zweier geschlossenen konvexen Kurven in Bezug auf einen Punkt, Tôhoku Math. J. 10 (1916), 99-103. Zbl46.1117.01
  3. [3] P. J. Kelly, Curves with a kind of constant width, Amer. Math. Monthly 64 (1957), 333-336. Zbl0080.15602
  4. [4] V. Klee, Can a plane convex body have two equichordal points?, Amer. Math. Monthly 76 (1969), 54-55. 
  5. [5] V. Klee, Some unsolved problems in plane geometry, Math. Mag. 52 (3) (1979), 131-145. Zbl0418.51005
  6. [6] R. Langevin, G. Levitt et H. Rosenberg, Hérissons et multihérissons ( Enveloppes paramétrées par leur application de Gauss), in: Singularities (Warsaw, 1985), Banach Center Publ. 20, PWN, Warszawa, 1988, 245-253. Zbl0658.53004
  7. [7] Y. Martinez-Maure, Sur les hérissons projectifs (enveloppes paramétrées par leur application de Gauss), Bull. Sci. Math., to appear. 
  8. [8] C. M. Petty and J. M. Crotty, Characterization of spherical neighborhoods, Canad. J. Math. 22 (1970), 431-435. Zbl0195.12603
  9. [9] R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge Univ. Press, 1993. Zbl0798.52001
  10. [10] E. Wirsing, Zur Analytizität von Doppelspeichkurven, Arch. Math. (Basel) 9 (1958), 300-307. Zbl0083.38404

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