Circles in Arbitrary Triangles

The following pictures show n unit circles packed inside the triangle with smallest known area A (with sides a, b, and c). For n not shown, the best known packing is in an equilateral triangle.

 2. 4. 7. A = 6 + 4√2 = 11.656+a = 2 + 2√2     b = 2 + 2√2     c = 4 + 2√2 David W. Cantrell     June 2007 A = 9 + 6√3 = 19.392+a = 3 + √3     b = 3 + 3√3     c = 6 + 2√3 David W. Cantrell     June 2007 A = 31.212+a = 7.946+     b = 7.946+     c = 10.352+ David W. Cantrell     June 2007

 8. 11. 12. A = 35.936+a = 8.038+     b = 9.018+     c = 11.270+ David W. Cantrell     June 2007 A = 47.003+a = 9.547+     b = 10.170+     c = 12.081+ David W. Cantrell     June 2007 A = 51.304+a = 9.875+     b = 10.666+     c = 12.792+ David W. Cantrell     June 2007

 13. 16. 17. A = 54.894+a = 10.632+     b = 11.333+     c = 11.922+ David W. Cantrell     June 2007 A = 21 + 26√3 = 66.033+a = 7 + √3     b = 3 + 7√3     c = 14 + 2√3 David W. Cantrell     June 2007 A = 70.275+a = 11.673+     b = 12.434+     c = 14.775+ David W. Cantrell     June 2007

 18. 19. 22. A = 74.803+a = 12.723+     b = 13.171+     c = 13.577+ David W. Cantrell     June 2007 A = 77.346+a = 12.892+     b = 13.169+     c = 14.130+ David W. Cantrell     June 2007 A = 89.127+a = 13.211+     b = 14.540+     c = 15.579+ David W. Cantrell     June 2007

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