Circles Covering Circles

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

 n=1 r = 1Trivial. n=3 r = 2 / √3 = 1.154+Trivial. n=4 r = √2 = 1.414+Trivial. n=5 r = 1.641+Proved by Károly Bezdekin 1983.

 n=6 r = 1.798+Proved by Károly Bezdekin 1979. n=7 r = 2Trivial. n=8 r = 2.246+Proved by Gábor Fejes Tóthin 1996. n=9 r = √2 + 1 = 2.414+Proved by Gábor Fejes Tóthin 1996.

 n=10 r = 2.532+Proved by Gábor Fejes Tóthin 2005. n=11 r = 2.631+Found by Hans Melissenin 1997. n=12 r = 2.769+Found by Hans Melissenin 1997. n=13 r = 2.884+Found by Jeremy Tanin 2018.

 n=14 r = 3.014+Found by Jeremy Tanin 2018. n=15 r = 3.143+Found by Jeremy Tanin 2018. n=16 r = 3.244+Found by Jeremy Tanin 2018. n=17 r = 3.349+Found by Jeremy Tanin 2018.

 n=18 r = 3.446+Found by Jeremy Tanin 2018. n=19 r = √13 = 3.605+Found by Jeremy Tanin 2018. n=20 r = 3.692+Found by Jeremy Tanin 2018. n=21 r = 3.804+Found by Jeremy Tanin 2018.

 n=22 r = 3.948+Found by Jeremy Tanin 2018. n=23 r = 4.000+Found by Jeremy Tanin 2018. n=24 r = 4.076+Found by Jeremy Tanin 2018. n=25 r = √6 + √3 = 4.181+Found by Jeremy Tanin 2018.