Geometriae Dedicata

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

Besicovitch triangles extended

  • Y. MovshovichEmail author
Original Paper


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.


Rectifiable unit arc Worm Worm cover 

Mathematics Subject Classification (2000)



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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentEastern Illinois UniversityCharlestonUSA

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