Triangles in Hexagons

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 = √((6+√33)/12) = .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.

1.		2.		3.
s = 1/√3 = .577+ Trivial.		s = √3/2 = .866+ Trivial.		s = √((6+√33)/12) = .989+ Found by Erich Friedman in April 2005.

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.