volume 33, issue 3, P369-393 2004
DOI: 10.1007/s00454-004-1145-z
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Abstract: Each convex planar set K has a perimeter C, a minimum width E, an area A, and a diameter D. The set of points (E, C, A 1/2 , D) corresponding to all such sets is shown to occupy a cone in the non-negative orthant of R 4 with its vertex at the origin. Its three-dimensional cross section S in the plane D = 1 is investigated. S lies in a rectangular parallelepiped in R 3 . Results of Lebesgue, Kubota, Fukasawa, Sholander, and Hemmi are used to determine some of the boundary surfaces of S, and new results are giv…

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