Packing up to 50 equal circles in a square

Packing up to 50 equal circles in a square

0.00 Avg rating0 Votes
Article ID: iaor19981085
Country: United States
Volume: 18
Issue: 1
Start Page Number: 111
End Page Number: 120
Publication Date: Jul 1997
Journal: Discrete and Computational Geometry
Authors: ,
Keywords: combinatorial analysis
Abstract:

The problem of maximizing the radius of n equal circles that can be packed into a given square is a well-known geometrical problem. An equivalent problem is to find the largest distance d, such that n points can be placed into the square with all mutual distances at least d. Recently, all optimal packings of at most 20 circles in a square were exactly determined. In this paper, computational methods to find good packings of more than 20 circles are discussed. The best packings found with up to 50 circles are displayed. A new packing of 49 circles settles the proof that when n is a square number, the best packing is the square lattice exactly when n ≤ 36.

Reviews

Required fields are marked *. Your email address will not be published.