TY - JOUR
T1 - Covering a rectangle with six and seven equal circles
AU - Melissen, J.B.M.
AU - Schuur, P.C.
PY - 2000
Y1 - 2000
N2 - In a recent article (Heppes and Melissen, Period. Math. Hungar. 34 (1997) 63–79), Heppes and Melissen have determined the thinnest coverings of a rectangle with up to five equal circles and also for seven circles if the aspect ratio of the rectangle is either between 1 and 1.34457…, or larger than 3.43017… . In this paper we extend these results. For the gap in the seven circles case we present thin coverings that we conjecture to be optimal. For six circles we determine the thinnest possible covering if the aspect ratio is larger than 3.11803… . Furthermore, for six and seven circles, we give thin coverings for the remaining range of values, thereby extending our previous conjecture for the square (Melissen and Schuur, Electron. J. Combin. 3 (1996) R32). [6].
AB - In a recent article (Heppes and Melissen, Period. Math. Hungar. 34 (1997) 63–79), Heppes and Melissen have determined the thinnest coverings of a rectangle with up to five equal circles and also for seven circles if the aspect ratio of the rectangle is either between 1 and 1.34457…, or larger than 3.43017… . In this paper we extend these results. For the gap in the seven circles case we present thin coverings that we conjecture to be optimal. For six circles we determine the thinnest possible covering if the aspect ratio is larger than 3.11803… . Furthermore, for six and seven circles, we give thin coverings for the remaining range of values, thereby extending our previous conjecture for the square (Melissen and Schuur, Electron. J. Combin. 3 (1996) R32). [6].
U2 - 10.1016/S0166-218X(99)00130-4
DO - 10.1016/S0166-218X(99)00130-4
M3 - Article
SN - 0166-218X
VL - 99
SP - 149
EP - 156
JO - Discrete applied mathematics
JF - Discrete applied mathematics
IS - 1-3
ER -