| Title:
|
Translative packing of a convex body by sequences of its homothetic copies (English) |
| Author:
|
Januszewski, Janusz |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
89-92 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Every sequence of positive or negative homothetic copies of a planar convex body $C$ whose total area does not exceed $0.175$ times the area of $C$ can be translatively packed in $C$. (English) |
| Keyword:
|
translative packing |
| Keyword:
|
convex body |
| MSC:
|
52C15 |
| idZBL:
|
Zbl 1212.52020 |
| idMR:
|
MR2432845 |
| . |
| Date available:
|
2008-07-24T13:17:36Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116925 |
| . |
| Reference:
|
[1] Böröczky, Jr.: Finite packing and covering.Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge 154 (2004). Zbl 1061.52011, MR 2078625 |
| Reference:
|
[2] Januszewski, J.: A note on translative packing a triangle by sequences of its homothetic copies.Period. Math. Hungar. 52 (2) (2006), 27–30. Zbl 1127.52023, MR 2265648, 10.1007/s10998-006-0010-7 |
| Reference:
|
[3] Januszewski, J.: Translative packing of a convex body by sequences of its positive homothetic copies.Acta Math. Hungar. 117 (4) (2007), 349–360. Zbl 1174.52010, MR 2357419, 10.1007/s10474-007-6121-7 |
| Reference:
|
[4] Lassak, M.: Approximation of convex bodies by rectangles.Geom. Dedicata 47 (1993), 111–117. Zbl 0779.52007, MR 1230108, 10.1007/BF01263495 |
| Reference:
|
[5] Meir, A., Moser, L.: On packing of squares and cubes.J. Combin. Theory 5 (1968), 126–134. MR 0229142, 10.1016/S0021-9800(68)80047-X |
| Reference:
|
[6] Moon, J. W., Moser, L.: Some packing and covering theorems.Colloq. Math. 17 (1967), 103–110. Zbl 0152.39502, MR 0215197 |
| Reference:
|
[7] Novotny, P.: A note on packing clones.Geombinatorics 11 (1) (2001), 29–30. Zbl 1005.52010, MR 1837580 |
| . |
