Triangles in Hexagons

The following pictures show n equilateral triangles with side 1 packed inside the smallest known regular hexagon (of side length s ).


1.            2.            3.
s = 1/√3 = .577+
Trivial.
s = √3/2 = .866+
Trivial.
s = .989+
Found by Erich Friedman
in April 2005.


4.            5.            6.
s = 1
Trivial.
s = 1
Trivial.
s = 1
Trivial.


7.            8.            9.
s = 1.277+
Found by David W. Cantrell
in May 2005.
s = 1.356+
Found by David W. Cantrell
in July 2012.
s = 1.434+
Found by Erich Friedman
in April 2005.


10.            11.            12.
s = 3/2 = 1.500
Found by Erich Friedman
in April 2005.
s = 3/2 = 1.500
Found by Erich Friedman
in April 2005.
s = 1.627+
Found by Maurizio Morandi
in May 2008.


13.            14.            15.
s = 5/3 = 1.666+
Found by Erich Friedman
in April 2005.
s = 1.725+
Found by DWC after MM
in August 2012.
s = 7/4 = 1.750
Found by Erich Friedman
in April 2005.


16.            17.            18.
s = 9/5 = 1.800
Found by Maurizio Morandi
in April 2008.
s = 11/6 = 1.833+
Found by Maurizio Morandi
in April 2008.
s = 17/9 = 1.888+
Found by Maurizio Morandi
in April 2008.


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