Accessible Requires Authentication Published by De Gruyter June 9, 2017

Drapeable unit arcs fit in the unit 30° sector

Yevgenya Movshovich and John E. Wetzel
From the journal Advances in Geometry

Abstract

We show that a 30° circular sector of unit radius contains an isometric copy of every drapeable unit arc, and we describe the family of drapeable exit arcs of unit length in the sector. The conjecture that this sector is a cover for the family of all unit arcs remains unresolved.


Communicated by: S. H. Weintraub


Acknowledgements

We want to express our gratitude to Peter Moses (Redditch, Worcestershire, UK) and to Frederick Norwood (East Tennessee State University) for some helpful comments. We want also to acknowledge others who have claimed some progress on the question of whether the 30° unit sector is a cover for all unit arcs but have not published their arguments. They are Professors Patrick Coulton (Eastern Illinois University), George Poole (East Tennessee University), and Wacharin Wichirimala (Chulalongkorn University). In addition we are grateful for the supportive comments at significant times by our colleague and friend J. Ralph Alexander. Finally, we would like to express our gratitude for the exceptional efforts made by the referee, which helped us greatly to improve the article.

References

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Received: 2015-4-15
Revised: 2016-2-4
Published Online: 2017-6-9
Published in Print: 2017-10-26

© 2017 by Walter de Gruyter Berlin/Boston