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On Outwardly Simple Line Families

Published online by Cambridge University Press:  20 November 2018

Jack Ceder
Jack Ceder*
Affiliation:
University of California, Santa Barbara
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In (5) Hammer and Sobczyk defined an outwardly simple line family in the plane as a family of lines in the plane having the property that each point outside some given circle lies on exactly one line of the family, and they characterized planar outwardly simple line families as follows (5): the extended diameters of a convex body, whose boundary has no pair of parallel line segments in it, form an outwardly simple line family; moreover, each outwardly simple line family is the family of extended diameters of a convex body having constant width.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 1 - 11
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Eggleston, H. G., Problems in Euclidean space: Application of convexity (New York, 1957).Google Scholar
2. Grünbaum, B., Measures of symmetry for convex sets , Proc. Symposium on Convex Sets, Seattle, 1961. In press.Google Scholar
3. Hammer, P. C., Diameters of convex bodies, Proc. Amer. Math. Soc, 5 (1954), 304–306.Google Scholar
4. Hammer, P. C., Convex curves of constant Minkowski breadth, to appear in Amer. Math. Soc. Symposium on Pure Math., 1963.Google Scholar
5. Hammer, P. C. and Sobczyk, A., Planar line families I, Proc. Amer. Math. Soc, 4 (1953), 226–233.Google Scholar
6. Hammer, P. C. and Sobczyk, A., Planar line families II, Proc. Amer. Math. Soc, 4 (1953), 341–349.Google Scholar
7. Neumann, B. H., On some affine invariants of closed convex regions, J. London Math. Soc, 14(1939), 262–272.Google Scholar
8. Smith, T. J., Line families in the plane, Univ. of Wisconsin Thesis, 1961.Google Scholar
9. Sobczyk, A., Simple line families, Pac J. Math., 6 (1956), 541–552.Google Scholar