Tans in Circles

The following pictures show n tans with leg 1 packed inside the smallest known circle (of radius r).


1.
           2.
           3.
r = 1/√2 = .707+
Trivial.
r = 1/√2 = .707+
Trivial.
r = (6 + √2)/8 = .926+
Found by Serhiy Grabarchuk
in April 2005.


4.
           5.
           6.
r = 1
Trivial.
r = 1.125+
Found by Maurizio Morandi
in July 2007.
r = 1.198+
Found by Maurizio Morandi
in July 2007.


7.
           8.
           9.
r = 1.26287+
Found by Jake Loyd
in June 2026.
r = √(1+1/√2) = 1.306+
Found by Serhiy Grabarchuk
in April 2005.
r = 1.37381+
Found by Thomas Greenleaf
in June 2026.


10.
           11.
           12.
r = 1.42230+
Found by Thomas Greenleaf
in June 2026.
r = 1.480+
Found by David W. Cantrell
in August 2007.
r = 1.50878+
Found by Jake Loyd
in June 2026.


13.
           14.
           15.
r = 1.55348+
Found by Jake Loyd
in June 2026.
r = √10/2 = 1.581+
Found by Serhiy Grabarchuk
in April 2005.
r = 1.66443+
Found by Jake Loyd
in June 2026.


16.
           17.
           18.
r = 1.74180+
Found by Jake Loyd
in June 2026.
r = 1.80067+
Found by Jake Loyd
in June 2026.
r = 1.83366+
Found by Jake Loyd
in June 2026.


19.
           20.
r = 1.88814+
Found by Jake Loyd
in June 2026.
r = 1.93833+
Found by Jake Loyd
in June 2026.