The densest packing of equal circles into a parallel strip
نویسندگان
چکیده
منابع مشابه
Densest Packing of Equal Circles Inthe Hyperbolic
We propose a deenition of density for packings of circles of xed radius in the hyperbolic plane, and prove that for all but countably many radii, optimally dense packings must have low symmetry.
متن کاملParallel greedy algorithms for packing unequal circles into a strip or a rectangle
Given a finite set of circles of different sizes we study the Strip Packing Problem (SPP) as well as the Knapsack Problem (KP). The SPP asks for a placement of all circles (without overlap) within a rectangular strip of fixed width so that the variable length of the strip is minimized. The KP requires packing of a subset of the circles in a rectangle of fixed dimensions so that the wasted area ...
متن کاملThe Densest Packing of 13 Congruent Circles in a Circle
The densest packings of n congruent circles in a circle are known for n ≤ 12 and n = 19. In this article we examine the case of 13 congruent circles. We show that the optimal configurations are identical to Kravitz’s conjecture. We use a technique developed from a method of Bateman and Erdős, which proved fruitful in investigating the cases n = 12 and 19. MSC 2000: 52C15
متن کاملDensest Packing of Equal Spheres in Hyperbolic Space
We propose a method to analyze the density of packings of spheres of fixed radius in the hyperbolic space of any dimension m ≥ 2, and prove that for all but countably many radii, optimally dense packings must have low symmetry.
متن کاملA better packing of ten equal circles in a square
Let S be a square of side s in the Euclidean plane. A pucking of circles in S is nothing else but a finite family of circular disks included in S whose interiors are pairwise disjoints. A natural problem related with such packings is the description of the densest ones; in particular, what is the greatest value of the common radius r of n circles forming a packing of S? Clearly, the centres of ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1991
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02574677