Packing $13$ unit circles in an equilateral triangle
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The side length of the smallest equilateral triangle into which $13$ unit circles can be packed.
Lower bound:
Unknown
Upper bound:
$4+\frac{2\sqrt{6}}{3} + \frac{10\sqrt{3}}{3}$
(≈11.4065)
Updates
-
1993-12
Upper bound: $4+\frac{2\sqrt{6}}{3} + \frac{10\sqrt{3}}{3}$
(≈11.4065)
Melissen, H. (1993). Densest packings of congruent circles in an equilateral triangle. The American Mathematical Monthly, 100(10), 916-925.
[via Circles in Triangles, Erich Friedman]