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 = 1.265+
Found by Maurizio Morandi
in August 2007.
r = √(1+1/√2) = 1.306+
Found by Serhiy Grabarchuk
in April 2005.
r = 1.377+
Found by David W. Cantrell
in August 2007.


10.
           11.
           12.
r = 1.428+
Found by Maurizio Morandi
in July 2007.
r = 1.480+
Found by David W. Cantrell
in August 2007.
r = 1.509+
Found by David W. Cantrell
in August 2007.


13.
           14.
           15.
r = 1.559+
Found by Serhiy Grabarchuk
in April 2005.
r = √10/2 = 1.581+
Found by Serhiy Grabarchuk
in April 2005.
r = 1.667+
Found by Maurizio Morandi
in July 2007.


16.
           17.
           18.
r = 1.746+
Found by David W. Cantrell
in August 2007.
r = 1.806+
Found by David W. Cantrell
in August 2007.
r = 1.834+
Found by David W. Cantrell
in August 2007.


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