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Sectorial Covers for Curves of Constant Length

Published online by Cambridge University Press:  20 November 2018

John E. Wetzel
John E. Wetzel*
Affiliation:
University of Illinois, Urbana, Illinois
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In answer to a question raised by Leo Moser, A. Meir proved some years ago that every plane arc of unit length lies in some closed semidisk of radius ½. His elegant, unpublished argument is reproduced here with his kind permission.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 3 , September 1973 , pp. 367 - 375
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Blaschke, W., Über den grössten Kreis in einer konvexen Punktmenge, Jber. Deutsch. Math.-Verein. 23 (1914), 369–374.Google Scholar
2. Croft, H. T., Research problems, (Mimeographed), Cambridge, England, 1967.Google Scholar
3. Croft, H. T., Addenda, (Mimeographed), Cambridge, England, 1969.Google Scholar
4. Jones, J. P. and Schaer, J., The worm problem, Univ. of Calgary Research Paper No. 100, Calgary, Alberta, Canada, 1970.Google Scholar
5. Mitrinović, D. S., Elementary inequalities, Noordhoff, Groningen, 1964.Google Scholar
6. Moser, Leo, Poorly formulated unsolved problems of combinatorial geometry. (Mimeographed.)Google Scholar
7. Pál, Julius, Ein Minimumproblem für Ovale, Math. Ann. 83 (1921), 311–319.Google Scholar
8. Schaer, Jonathan, The broadest curve of length 1, Univ. of Calgary Mathematical Research Paper No. 52, Calgary, Alberta, Canada, 1968.Google Scholar
9. Wetzel, John E., Triangular covers for closed curves of constant length, Elem. Math. 24 (1970), 78–82.Google Scholar
10. Yaglom, I. M. and Boltyanskiá, V. G., Convex figures, Holt, New York, 1961.Google Scholar