Bodies of constant width in arbitrary dimension
نویسندگان
چکیده
منابع مشابه
Bodies of constant width in arbitrary dimension
We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n − 1)dimensional projection being given. We give a number of examples, like a four-dimensional body of constant width whose 3D-projection is the classical Meissner’s body.
متن کاملEfficient Lattice Width Computation in Arbitrary Dimension
We provide an algorithm for the exact computation of the lattice width of an integral polygon K in linear-time with respect to the size of K. Moreover, we describe how this new algorithm can be extended to an arbitrary dimension thanks to a greedy approach avoiding complex geometric processings.
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 کاملNakajima’s Problem: Convex Bodies of Constant Width and Constant Brightness
For a convex body K ⊂ Rn, the kth projection function of K assigns to any k-dimensional linear subspace of Rn the k-volume of the orthogonal projection of K to that subspace. Let K and K0 be convex bodies in Rn, and let K0 be centrally symmetric and satisfy a weak regularity and curvature condition (which includes all K0 with ∂K0 of class C2 with positive radii of curvature). Assume that K and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 2007
ISSN: 0025-584X,1522-2616
DOI: 10.1002/mana.200510512