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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