The following pictures show n equilateral triangles with side 1 packed inside the smallest known equilateral triangles (of side length s ). Most of these have not been proven.

1. | 2. | 3. | ||

s = 1 Trivial. | s = 2 Trivial. | s = 2 Trivial. |

4. | 5. | 6. | ||

s = 2 Trivial. | s = 1 + √3 = 2.732+ Proved by Erich Friedman in 1997. | s = 13/8 + 3√13/8 = 2.977+ Found by Maurizio Morandi in August 2008. |

7. | 8. | 9. | ||

s = 3 Found by Erich Friedman in 1997. | s = 3 Found by Erich Friedman in 1997. | s = 3 Trivial. |

10. | 11. | 12. | ||

s = 3.5 Found by Erich Friedman in 1997. | s = 9/4 + 9√21/28 = 3.722+ Found by Erich Friedman in 1997. | s = 2 + 2cos(π/9) = 3.879+ Found by David W. Cantrell in July 2007. |

13. | 14. | 15. | ||

s = 3.992+ Found by Maurizio Morandi in May 2008. | s = 4 Trivial | s = 4 Trivial |

16. | 17. | 18. | ||

s = 4 Trivial | s = 4.465+ Found by Maurizio Morandi in May 2008. | s = 4.5 Found by Erich Friedman in 1997. |

19. | 20. | 21. | ||

s = 14/3 = 4.666+ Found by Maurizio Morandi in May 2008. | s = 33/8 + 9√21/56 = 4.861+ Found by Maurizio Morandi in May 2008. | s = 4.923+ Found by Maurizio Morandi in May 2008. |

22. | 23. | 24. | ||

s = 4.996+ Found by Maurizio Morandi in May 2008. | s = 5 Trivial | s = 5 Trivial |

25. | 26. | 27. | ||

s = 5 Trivial | s = 5.408+ Found by Maurizio Morandi in May 2008. | s = 5.5 Found by Erich Friedman in 1997. |

28. | 29. | 30. | ||

s = 5.5 Found by Erich Friedman in 1997. | s = 17/3 = 5.666+ Found by David W. Cantrell in July 2007. | s = 23/4 = 5.75 Found by Maurizio Morandi in May 2008. |