The following pictures show n circles with the largest possible sum of radii packed inside a unit equilateral triangle.

1. | 2. | 3. | ||

Σ r = √3/6 = .288+ Trivial. | Σ r = 2√3/9 = .384+ Trivial. | Σ r = (3√3 – 3) / 4 = .549+ Trivial. |

4. | 5. | 6. | ||

Σ r = .617+ Found by David W. Cantrell in June 2011. | Σ r = .693+ Found by David W. Cantrell in June 2011. | Σ r = 6 – 3√3 = .803+ Trivial. |

7. | 8. | 9. | ||

Σ r = .855+ Found by David W. Cantrell in June 2011. | Σ r = .912+ Found by David W. Cantrell in June 2011. | Σ r = .976+ Found by David W. Cantrell in June 2011. |

10. | 11. | 12. | ||

Σ r = (15 – 5√3) / 6 = 1.056+ Trivial. | Σ r = 1.098+ Found by David W. Cantrell in June 2011. | Σ r = 1.143+ Found by David W. Cantrell in June 2011. |

13. | 14. | 15. | ||

Σ r = 1.191+ Found by David W. Cantrell in June 2011. | Σ r = 1.243+ Found by David W. Cantrell in June 2011. | Σ r = (60 – 15√3) / 26 = 1.308+ Trivial. |

16. | 17. | 18. | ||

Σ r = 1.343+ Found by David W. Cantrell in June 2011. | Σ r = 1.381+ Found by David W. Cantrell in June 2011. | Σ r = 1.420+ Found by David W. Cantrell in June 2011. |

19. | 20. | 21. | ||

Σ r = 1.462+ Found by David W. Cantrell in June 2011. | Σ r = 1.505+ Found by David W. Cantrell in July 2011. | Σ r = (105 – 21√3) / 44 = 1.559+ Trivial. |

22. | 23. | 24. | ||

Σ r = 1.589+ Found by David W. Cantrell in July 2011. | Σ r = 1.622+ Found by David W. Cantrell in July 2011. | Σ r = 1.655+ Found by David W. Cantrell in July 2011. |

25. | 26. | 27. | ||

Σ r = 1.690+ Found by David W. Cantrell in July 2011. | Σ r = 1.727+ Found by David W. Cantrell in July 2011. | Σ r = 1.763+ Found by David W. Cantrell in July 2011. |