The following pictures show n unit circles packed inside the smallest known circle (of radius r).

1. | 2. | 3. | ||

r = 1 Trivial. | r = 2 Trivial. | r = 1 + 2 / √3 = 2.154+ Trivial. |

4. | 5. | 6. | ||

r = 1 + √2 = 2.414+ Trivial. | r = 2.701+ Proved by Graham in 1968. | r = 3 Proved by Graham in 1968. |

7. | 8. | 9. | ||

r = 3 Proved by Graham in 1968. | r = 3.304+ Proved by Braaksma in 1963. | r = 3.613+ Proved by Pirl in 1969. |

10. | 11. | 12. | ||

r = 3.813+ Proved by Pirl in 1969. | r = 3.923+ Proved by Melissen in 1994. | r = 4.029+ Found by Kravitz in 1967. |

13. | 14. | 15. | ||

r = 2 + √5 = 4.236+ Proved by F. Fodor in 2003. | r = 4.328+ Found by Goldberg in 1971. | r = 4.521+ Found by Kravitz in 1967. |

16. | 17. | 18. | ||

r = 4.615+ Found by Goldberg in 1971. | r = 4.792+ Found by Reis in 1975. | r = 1 + √2 + √6 = 4.863+
Found by Kravitz in 1967. |

19. | 20. | ||

r = 1 + √2 + √6 = 4.863+ Proved by F. Fodor in 1999. | r = 5.122+ Found by Goldberg in 1971. |