About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Paper
ON curves contained in convex subsets of the plane
Abstract
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. © 2005 Akadémiai Kiadó, Budapest.