Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T18:43:57.132Z Has data issue: false hasContentIssue false

Sectorial Covers for Curves of Constant Length

Published online by Cambridge University Press:  20 November 2018

John E. Wetzel*
Affiliation:
University of Illinois, Urbana, Illinois
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 His elegant, unpublished argument is reproduced here with his kind permission.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
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Blaschke, W., Über den grössten Kreis in einer konvexen Punktmenge, Jber. Deutsch. Math.-Verein. 23 (1914), 369374.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), 311319.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), 7882.Google Scholar
10. Yaglom, I. M. and Boltyanskiá, V. G., Convex figures, Holt, New York, 1961.Google Scholar