The following pictures show n unit circles packed inside the smallest hexagon (of side length s).

1. | 2. | 3. | ||

s = 2/√3 = 1.154+ Trivial. | s = 1 + 2/√3 = 2.154+ Trivial. | s = 4/√3 = 2.309+ Trivial. |

4. | 5. | 6. | ||

s = 2/√3 + 4/√7 = 2.666+ Found by Shahriar Manzoor in April 2002. | s = 2.999+ Found by Erich Friedman in 1999. | s = 2 + 2/√3 = 3.154+ Trivial. |

7. | 8. | 9. | ||

s = 2 + 2/√3 = 3.154+ Trivial. | s = 3.709+ Found by David W. Cantrell in July 2002. | s = 20/7 + 2/√3 = 4.011+ Found by David W. Cantrell in July 2002. |

10. | 11. | 12. | ||

s = 4.119+ Found by David W. Cantrell in July 2002. | s = 2 + 4/√3 = 4.309+ Found by Erich Friedman in 1999. | s = 2 + 4/√3 = 4.309+ Found by Erich Friedman in 1999. |

13. | 14. | 15. | ||

s = 8/√3 = 4.618+ Found by Erich Friedman in 1999. | s = 2 + 2/√3 + 4/√7 = 4.666+ Found by David W. Cantrell in July 2002. | s = 4.961+ Found by David W. Cantrell in January 2006. |

16. | 17. | 18. | ||

s = 4.999+ Found by David W. Cantrell in July 2002. | s = 5.133+ Found by David W. Cantrell in January 2006. | s = 4 + 2/3 = 5.154+ Trivial. |

19. | 20. | 21. | ||

s = 4 + 2/√3 = 5.154+ Trivial. | s = 5.676+ Found by David W. Cantrell in July 2012. | s = 5.709+ Found by David W. Cantrell in July 2012. |

22. | 23. | 24. | ||

s = 5.952+ Found by David W. Cantrell in July 2012. | s = 34/7 + 2/√3 = 6.011+ Found by David W. Cantrell in July 2012. | s = 6.119+ Found by David W. Cantrell in July 2012. |