On curves contained in convex subsets of the plane

Don Coppersmith; Győző Nagy; Sasha Ravsky

doi:10.1556/sscmath.42.2005.1.9

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 42: Issue 1

On curves contained in convex subsets of the plane

Authors:

Don Coppersmith

Don Coppersmith Department of Mathematical Sciences, IBM Thomas J. Watson Research Center Yorktown Heights NY 10598, U.S.A

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Győző Nagy

Győző Nagy Technical Center, Raiffeisen Hungary H-1158 Budapest, Késmárk u. 11-13, Hungary

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, and

Sasha Ravsky

Sasha Ravsky Department of Mathematics, Ivan Franko Lviv National University Universytetska 1, Lviv, 79000, Ukraine

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Pages:: 107–112

Online Publication Date:: 22 Jul 2005

Publication Date:: 01 Jan 2005

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.42.2005.1.9

Keywords:: Convex body; Convex body; Convex body; strictly convex body

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If K' ? K are convex bodies of the plane then the perimeter of K' is not greater than the perimeter of K. We obtain the following generalization of this fact. Let K be a convex compact body of the plane with perimeter p and diameter d and let r ? 1 be an integer. Let s be the smallest number such that for any curve of length greater than s contained in K there is a straight line intersecting the curve at least in r+1 different points. Then s = rp/2 if r is even and s = (r-1) p/2 + d if r is odd.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

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Studia Scientiarum Mathematicarum Hungarica
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