Simple Polygons of Maximum Perimeter Contained in a Unit Disk
نویسندگان
چکیده
منابع مشابه
On the Perimeters of Simple Polygons Contained in a Plane Convex Body
A simple n-gon is a polygon with n edges such that each vertex belongs to exactly two edges and every other point belongs to at most one edge. Brass, Moser and Pach [2, Problem 3, p. 437] asked the following question: For n ≥ 5 odd, what is the maximum perimeter of a simple n-gon contained in a Euclidean unit disk? In 2009, Audet, Hansen and Messine [1] answered this question, and showed that t...
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The paper answers the three distinct questions of maximizing the perimeter, diameter and area of equilateral unit-width convex polygons. The solution to each of these problems is trivially unbounded when the number of sides is even. We show that when this number is odd, the optimal solution to these three problems is identical, and arbitrarily close to a trapezoid. The paper also considers the ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2008
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-008-9093-7