Circles Covering Triangles

The following pictures show n unit circles covering the largest known equilateral triangle (of side s ).

1. 2. 3.
s = √3 = 1.732+
Trivial. s = 2
Trivial. s = 2√3 = 3.464+
Trivial.

4. 5. 6.
s = 2 + √3 = 3.732+
Proved by Hans Melissen
in 1997. s = 4
Proved by Hans Melissen
in 1997. s = 3√3 = 5.196+
Proved by Hans Melissen
in 1997.

7. 8. 9.
s = 5.398+
Found by P. Schuur
in 1997. s = 5.649+
Found by P. Schuur
in 1997. s = 6
Proved by Hans Melissen
in 1997.

1.		2.		3.
s = √3 = 1.732+ Trivial.		s = 2 Trivial.		s = 2√3 = 3.464+ Trivial.

4.		5.		6.
s = 2 + √3 = 3.732+ Proved by Hans Melissen in 1997.		s = 4 Proved by Hans Melissen in 1997.		s = 3√3 = 5.196+ Proved by Hans Melissen in 1997.

7.		8.		9.
s = 5.398+ Found by P. Schuur in 1997.		s = 5.649+ Found by P. Schuur in 1997.		s = 6 Proved by Hans Melissen in 1997.