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 :
| Number of unit circles | Enclosing circle diameter | Density | Optimality | Diagram |
| 1 | 1 | 1.0000 | Trivially optimal. | |
| 2 | 2 | 0.5000 | Trivially optimal. | |
| 3 | ≈ 2.154... | 0.6466... | Trivially optimal. | |
| 4 | ≈ 2.414... | 0.6864... | Trivially optimal. | |
| 5 | ≈ 2.701... | 0.6854... | Trivially optimal. Also proved optimal by Graham | |
| 6 | 3 | 0.6666... | Trivially optimal. Also proved optimal by Graham | |
| 7 | 3 | 0.7777... | Trivially optimal. | |
| 8 | ≈ 3.304... | 0.7328... | Proved optimal by Pirl | |
| 9 | ≈ 3.613... | 0.6895... | Proved optimal by Pirl | |
| 10 | 3.813... | 0.6878... | Proved optimal by Pirl | |
| 11 | ≈ 3.923... | 0.7148... | Proved optimal by Melissen | |
| 12 | 4.029... | 0.7392... | Proved optimal by Fodor | |
| 13 | ≈ 4.236... | 0.7245... | Proved optimal by Fodor | |
| 14 | 4.328... | 0.7474... | Conjectured optimal. | |
| 15 | ≈ 4.521... | 0.7339... | Conjectured optimal. | |
| 16 | 4.615... | 0.7512... | Conjectured optimal. | |
| 17 | 4.792... | 0.7403... | Conjectured optimal. | |
| 18 | ≈ 4.863... | 0.7611... | Conjectured optimal. | |
| 19 | ≈ 4.863... | 0.8034... | Proved optimal by Fodor | |
| 20 | 5.122... | 0.7623... | Conjectured optimal. |