منابع مشابه
Packing up to 50 Equal Circles in a Square
The Hungarian mathematician Farkas Bolyai (1775–1856) published in his principal work (‘Tentamen’, 1832–33 [Bol04]) a dense regular packing of equal circles in an equilateral triangle (see Fig. 1). He defined an infinite packing series and investigated the limit of vacuitas (in Latin, the gap in the triangle outside the circles). It is interesting that these packings are not always optimal in s...
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 ...
متن کاملPacking Equal Circles in a Square: I. Solution Properties
In this paper some properties of optimal solutions for the problem of packing n equal circles into the unit square will be derived. In particular, properties, which must be satissed by at least one optimal solution of the problem and stating the intuitive fact that as many circles as possible should touch the boundary of the unit square, will be introduced.
متن کاملPacking equal circles in a square: a deterministic global optimization approach
In this paper the problem of packing n equal circles into the unit square will be considered. Starting from a general rectangular branch-and-bound algorithm, many tools, which exploit the special structure of the problem, will be introduced and discussed. Computational results will be presented and, in particular, the optimality within a given tolerance of best known solutions in the literature...
متن کاملNew results in the packing of equal circles in a square
The problem of nding the maximum diameter of n equal mutually disjoint circles inside a unit square is addressed in this paper. Exact solutions exist for only n = 1; : : : ; 9; 10; 16; 25; 36 while for other n only conjectural solutions have been reported. In this work a max{min optimization approach is introduced which matches the best reported solutions in the literature for all n 30, yields ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1997
ISSN: 0179-5376
DOI: 10.1007/pl00009306