Is a convex plane body determined by an isoptic?
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چکیده
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Covering the Plane with Congruent Copies of a Convex Body
It is shown that every plane compact convex set /f with an interior point admits a covering of the plane with density smaller than or equal to 8(2\/3 — 3)/3 = 1.2376043 For comparison, the thinnest covering of the plane with congruent circles is of density 2n/\Z21 = 1.209199576... (see R. Kershner [3]), which shows that the covering density bound obtained here is close to the best possible. It ...
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In the following, we cover some material from linear algebra. Proofs of those facts can be found in any text on linear algebra, for example [Leo98]. For a matrix A, let A T denote the transposed matrix. We remind the reader that for two matrices A and B, we have (AB) T = B T A T. Furthermore, for any three matrices A, B and C, we have (AB)C = A(BC). A matrix A ∈ IR n×n is symmetric if A T = A. ...
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ژورنال
عنوان ژورنال: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
سال: 2011
ISSN: 0138-4821,2191-0383
DOI: 10.1007/s13366-011-0074-2