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Disk covering problem : ウィキペディア英語版
Disk covering problem
The disk covering problem asks for the smallest real number r(n) such that n disks of radius r(n) can be arranged in such a way as to cover the unit disk. Dually, for a given radius ''ε'', one wishes to find the smallest integer ''n'' such that ''n'' disks of radius ''ε'' can cover the unit disk.〔.〕
The best solutions to date are as follows:
/2 = 0.707107...
| 90°, 4 reflections
|-
| 5
| 0.609382...
| 1 reflection
|-
| 6
| 0.555905...
| 1 reflection
|-
| 7
| 1/2 = 0.5
| 60°, 6 reflections
|-
| 8
| 0.445041...
| ~51.4°, 7 reflections
|-
| 9
| 0.414213...
| 45°, 8 reflections
|-
| 10
| 0.394930...
| 36°, 9 reflections
|-
| 11
| 0.380083...
| 1 reflection
|-
| 12
| 0.361141...
| 120°, 3 reflections
|}
==Method==
This is the best known layout strategy for r(9) and r(10):
File:DiscCoveringExample.svg

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「Disk covering problem」の詳細全文を読む



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