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Geometriae Dedicata

, Volume 159, Issue 1, pp 99–107 | Cite as

Besicovitch triangles extended

  • Y. MovshovichEmail author
Original Paper
  • 51 Downloads

Abstract

We extend the range of the base angle from \({ \scriptstyle \big[\arctan\sqrt{5\over3}\ ,\ {\pi\over 3}\big] }\) to \({\scriptstyle \big[ {\pi\over4} ,\ {\pi\over3}\big] }\) for the class of isosceles triangular worm covers obtained in Coulton and Movshovich (Geom Dedicata 123:79–88, 2006). We also show that each triangle has only one unit arc that does not fit in the interior of the triangle.

Keywords

Rectifiable unit arc Worm Worm cover 

Mathematics Subject Classification (2000)

52C15 

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References

  1. 1.
    Besicovitch S.: On arcs that cannot be covered by an open equilateral triangle of side 1. Math. Gaz 49, 286–288 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Coulton P., Movshovich Y.: Besicovitch triangles cover unit arcs. Geom. Dedicata 123, 79–88 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Graham, R.: Problem 41, Proceedings, 1963 Number Theory Conference, p. 98. University of Colorado, Boulder (1963)Google Scholar
  4. 4.
    Maki J.M., Wetzel J.E., Wichirimala W.: Drapeability. Discret. Comput. Geom. 34, 637–657 (2005)zbMATHCrossRefGoogle Scholar
  5. 5.
    Moser, L.: Poorly formulated unsolved problems in combinatorial geometry. mimeographed, undated, but about (1966)Google Scholar
  6. 6.
    Dan P.: The ellipse as an hypotrochoid. Math. Mag. 48, 228–230 (1975)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Wetzel J.E.: Fits and covers. Math. Mag 76, 349–363 (2003)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentEastern Illinois UniversityCharlestonUSA

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