On sets of constant width
نویسندگان
چکیده
منابع مشابه
Convex sets of constant width
A bounded convex set has constant width d iff any two parallel (and nonidentical) tangent planes to it have identical distance d from each other. Clearly balls have this property, but there are also other sets of constant width. This lecture was originally designed for a general audience as part of a series of lectures during the German “Year of Mathematics” 2008. It starts by presenting eviden...
متن کاملConvex Sets of Constant Width and -diameter
PETER HÄSTÖ, ZAIR IBRAGIMOV AND DAVID MINDA ABSTRACT. In this article we study -diameter of planar sets of constant width. We obtain analogues of the isodiametric inequality and the Blaschke-Lebesgue Theorem for -diameter of constant width sets. Namely, we prove that among all the sets of given constant width, disks have the smallest -diameter and Reuleaux triangles have the largest -diameter. ...
متن کاملFigures of Constant Width on a Chessboard
Every row and column of the board has only two occupied squares. But if we also consider the diagonals with slope +1 or −1, we see that each of them contains either zero or two squares of the figure. We say that Figure 1 has constant width three by rows and columns, and that Figure 2 has constant width two by rows, columns, and diagonals. The first figure is easy to generalize in the sense that...
متن کاملOn Minkowski Bodies of Constant Width
A metric set is entire if the addition of any point to the set increases the diameter. A convex body has constant width if all pairs of parallel supporting planes are the same distance apart. These concepts are known to be equivalent in euclidean space. The present paper shows that they are also equivalent in a minkowski space. A proof for this equivalence for the minkowski plane was given by M...
متن کاملIlluminating Spindle Convex Bodies and Minimizing the Volume of Spherical Sets of Constant Width
A subset of the d-dimensional Euclidean space having nonempty interior is called a spindle convex body if it is the intersection of (finitely or infinitely many) congruent d-dimensional closed balls. The spindle convex body is called a “fat” one, if it contains the centers of its generating balls. The core part of this paper is an extension of Schramm’s theorem and its proof on illuminating con...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1951
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1951-0041465-6