Geodesic
Sectorial Covers for Curves of Constant Length
Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 367-375

Voir la notice de l'article provenant de la source Cambridge University Press

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 1⁄2. His elegant, unpublished argument is reproduced here with his kind permission. 
Wetzel, John E. Sectorial Covers for Curves of Constant Length. Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 367-375. doi: 10.4153/CMB-1973-058-8
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[1] 1. Blaschke, W., Über den grössten Kreis in einer konvexen Punktmenge, Jber. Deutsch. Math.-Verein. 23 (1914), 369–374. Google Scholar

[2] 2. Croft, H. T., Research problems, (Mimeographed), Cambridge, England, 1967. Google Scholar

[3] 3. Croft, H. T., Addenda, (Mimeographed), Cambridge, England, 1969. Google Scholar

[4] 4. Jones, J. P. and Schaer, J., The worm problem, Univ. of Calgary Research Paper No. 100, Calgary, Alberta, Canada, 1970. Google Scholar

[5] 5. Mitrinović, D. S., Elementary inequalities, Noordhoff, Groningen, 1964. Google Scholar

[6] 6. Moser, Leo, Poorly formulated unsolved problems of combinatorial geometry. (Mimeographed.) Google Scholar

[7] 7. Pál, Julius, Ein Minimumproblem für Ovale, Math. Ann. 83 (1921), 311–319. Google Scholar

[8] 8. Schaer, Jonathan, The broadest curve of length 1, Univ. of Calgary Mathematical Research Paper No. 52, Calgary, Alberta, Canada, 1968. Google Scholar

[9] 9. Wetzel, John E., Triangular covers for closed curves of constant length, Elem. Math. 24 (1970), 78–82. Google Scholar

[10] 10. Yaglom, I. M. and Boltyanskiá, V. G., Convex figures, Holt, New York, 1961. Google Scholar

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