Dominoes in Circles

The following pictures show n dominoes (with short side 1) packed inside the smallest known circle (with radius r).


1.
           2.
           3.
r = √5/2 = 1.11803+
Trivial.
r = √2 = 1.41421+
Trivial.
r = √13/2 = 1.80277+
Trivial.


4.
           5.
           6.
r = 1.97949+
Found by Jonathan Viquerat
in May 2026
r = 2.18039+
Found by Jonathan Viquerat
in May 2026.
r = √5 = 2.23606+
Trivial.
 


7.
           8.
           9.
r = 2.51459+
Found by Jonathan Viquerat
in May 2026.
r = 2.65850+
Found by Yanis Gomes
in October 2026.
r = 2.76860+
Found by Jonathan Viquerat
in May 2026.


10.
           11.
           12.
r = 2.93547+
Found by Joshua Wolk
in September 2026.
r = 3.08701+
Found by Jonathan Viquerat
in August 2026.
r = √10 = 3.16227+
Found by Maurizio Morandi
in May 2026.


13.
           14.
           15.
r = 3.27584+
Found by Joshua Wolk in September 2026.
r = 3.37252+
Found by Joshua Wolk in September 2026.
r = 3.48514+
Found by Aapo Lipponen
in October 2026.


16.
           17.
           18.
r = √13 = 3.60555+
Found by Jonathan Viquerat
in May 2026.
r = √53/2 = 3.64005+
Found by Maurizio Morandi
in May 2026.
r = 3.77515+
Found by Joshua Wolk
in September 2026.


19.
           20.
           21.
r = 3.85676+
Found by Yanis Gomes
in October 2026.
r = 3.96669+
Found by Joshua Wolk
in September 2026.
r = 4.07666+
Found by Joshua Wolk
in September 2026.


22.
           23.
           24.
r = 4.12310+
Found by Joshua Wolk
in September 2026.
r = 4.19533+
Found by Yanis Gomes
in October 2026.
r = 4.27200+
Found by Jonathan Viquerat
in August 2026.


25.
           26.
           27.
r = 4.39150+
Found by Joshua Wolk
in September 2026.
r = 4.47213+
Found by Joshua Wolk
in September 2026.
r = 4.57608+
Found by Joshua Wolk
in September 2026.


28.
           29.
           30.
r = 4.62144+
Found by Joshua Wolk
in September 2026.
r = 4.69457+
Found by Joshua Wolk
in September 2026.
r = 4.76325+
Found by Joshua Wolk
in September 2026.


31.
           32.
           33.
r = 4.82244+
Found by Joshua Wolk
in September 2026.
r = 4.92443+
Found by Joshua Wolk
in September 2026.
r = 5.01036+
Found by Yanis Gomes
in October 2026.


34.
           35.
           36.
r = 5.06357+
Found by Joshua Wolk
in September 2026.
r = 5.12893+
Found by Joshua Wolk
in September 2026.
r = 5.17416+
Found by Joshua Wolk
in September 2026.


37.
           38.
           39.
r = 5.24663+
Found by Joshua Wolk
in September 2026.
r = 5.31712+
Found by Joshua Wolk
in September 2026.
r = 5.39564+
Found by Joshua Wolk
in September 2026.


40.
           41.
           42.
r = 5.47424+
Found by Yanis Gomes
in October 2026.
r = 5.53990+
Found by Yanis Gomes
in October 2026.
r = 5.58830+
Found by Joshua Wolk
in September 2026.


43.
           44.
           45.
r = 5.63788+
Found by Yanis Gomes
in October 2026.
r = 5.70087+
Found by Joshua Wolk
in September 2026.
r = 5.73703+
Found by Joshua Wolk
in September 2026.


46.
           47.
           48.
r = 5.77811+
Found by Joshua Wolk
in September 2026.
r = 5.86067+
Found by Joshua Wolk
in September 2026.
r = 5.94321+
Found by Yanis Gomes
in October 2026.


49.
           50.
r = 6.02440+
Found by Joshua Wolk
in September 2026.
r = 6.07141+
Found by Joshua Wolk
in September 2026.