Circles Covering Circles

The following pictures show n unit circles covering the largest known circle (of radius r ).

1. 3. 4.
r = 1
Trivial. r = 2 / √3 = 1.154+
Trivial. r = √2 = 1.414+
Trivial.

5. 6. 7.
r = 1.641+
Proved by Károly Bezdek
in 1983. r = 1.798+
Proved by Károly Bezdek
in 1979. r = 2
Trivial.

8. 9. 10.
r = 2.246+
Proved by Gábor Fejes Tóth
in 1996. r = √2 + 1 = 2.414+
Proved by Gábor Fejes Tóth
in 1996. r = 2.532+
Found by D. Nagy
in 1974.

11. 12.
r = 2.631+
Found by Hans Melissen
in 1997. r = 2.769+
Found by Hans Melissen
in 1997.

1.		3.		4.
r = 1 Trivial.		r = 2 / √3 = 1.154+ Trivial.		r = √2 = 1.414+ Trivial.

5.		6.		7.
r = 1.641+ Proved by Károly Bezdek in 1983.		r = 1.798+ Proved by Károly Bezdek in 1979.		r = 2 Trivial.

8.		9.		10.
r = 2.246+ Proved by Gábor Fejes Tóth in 1996.		r = √2 + 1 = 2.414+ Proved by Gábor Fejes Tóth in 1996.		r = 2.532+ Found by D. Nagy in 1974.

11.		12.
r = 2.631+ Found by Hans Melissen in 1997.		r = 2.769+ Found by Hans Melissen in 1997.