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.


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