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circle packing in a circle : ウィキペディア英語版
circle packing in a circle
Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle.
Minimum solutions (in case several minimal solutions have been shown to exist, only one variant appears in the table):〔(Erich Friedman, ''Circles in Circles'' on Erich's Packing Center )〕
\sqrt ≈ 2.154...
| 0.6466...
| Trivially optimal.
|
|- align=center
| 4
| 1+\sqrt ≈ 2.414...
| 0.6864...
| Trivially optimal.
|
|- align=center
| 5
| 1+\sqrt})} ≈ 2.701...
| 0.6854...
| Trivially optimal. Also proved optimal by Graham in 1968.〔
|
|- align=center
| 6
| 3
| 0.6667...
| Trivially optimal. Also proved optimal by Graham in 1968.〔
|
|- align=center
| 7
| 3
| 0.7778...
| Trivially optimal.
|
|- align=center
| 8
| 1+\frac)} ≈ 3.304...
| 0.7328...
| Proved optimal by Pirl in 1969.〔
|
|- align=center
| 9
| 1+\sqrt ≈ 3.613...
| 0.6895...
| Proved optimal by Pirl in 1969.〔
|
|- align=center
| 10
| 3.813...
| 0.6878...
| Proved optimal by Pirl in 1969.〔
|
|- align=center
| 11
| 1+\frac)} ≈ 3.923...
| 0.7148...
| Proved optimal by Melissen in 1994.〔
|
|- align=center
| 12
| 4.029...
| 0.7392...
| Proved optimal by Fodor in 2000.〔
| 120px
|- align=center
| 13
| 2 + \sqrt ≈4.236...
| 0.7245...
| Proved optimal by Fodor in 2003.〔
| 120x120px 120x120px
|- align=center
| 14
| 4.328...
| 0.7474...
| Conjectured optimal.〔
| 120px
|- align=center
| 15
| 1 + \sqrt} + 4 \sqrt}}} ≈ 4.521...
| 0.7339...
| Conjectured optimal.〔
| 120px
|- align=center
| 16
| 4.615...
| 0.7512...
| Conjectured optimal.〔
| 120px
|- align=center
| 17
| 4.792...
| 0.7403...
| Conjectured optimal.〔
| 120px
|- align=center
| 18
| 1+\sqrt+\sqrt ≈ 4.863...
| 0.7611...
| Conjectured optimal.〔
| 120px
|- align=center
| 19
| 1+\sqrt+\sqrt ≈ 4.863...
| 0.8034...
| Proved optimal by Fodor in 1999.〔
| 120px
|- align=center
| 20
| 5.122...
| 0.7623...
| Conjectured optimal.〔
| 120px
|}
==See also==

*Disk covering problem

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「circle packing in a circle」の詳細全文を読む



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