Thinnest Covering of a Circle by Eight, Nine, or Ten Congruent Circles
نویسنده
چکیده
Let rn be the maximum radius of a circular disc that can be covered by n closed unit circles. We show that rn = 1 + 2 cos(2π/(n−1)) for n = 8, n = 9, and n = 10.
منابع مشابه
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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تاریخ انتشار 2005