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 = 1.42227+
Found by Joshua Wolk
in September 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 = 1.73529+
Found by Joshua Wolk
in September 2026.
r = 1.79658+
Found by Joshua Wolk
in September 2026.
r = 1.83366+
Found by Jake Loyd
in June 2026.


19.
           20.
           21.
r = 1.88814+
Found by Jake Loyd
in June 2026.
r = 1.93426+
Found by Yanis Gomes
in October 2026.
r = 1.97214+
Found by Yanis Gomes
in October 2026.


22.
           23.
           24.
r = 2.02209+
Found by Yanis Gomes
in October 2026.
r = 2.05996+
Found by Yanis Gomes
in October 2026.
r = 2.10305+
Found by Yanis Gomes
in October 2026.


25.
           26.
           27.
r = 2.14386+
Found by Yanis Gomes
in October 2026.
r = 2.18226+
Found by Yanis Gomes
in October 2026.
r = 2.21049+
Found by Yanis Gomes
in October 2026.


28.
           29.
           30.
r = √5 = 2.23606+
Trivial.
r = 2.27984+
Found by Joost de Winter
in October 2026.
r = √(13+6√2)/2 = 2.31761+
Found by Maurizio Morandi
in October 2026.


31.
           32.
           33.
r = 2.36468+
Found by Yanis Gomes
in October 2026.
r = 2.41211+
Found by Yanis Gomes
in October 2026.
r = 2.44464+
Found by Yanis Gomes
in October 2026.


34.
           35.
           36.
r = 2.47732+
Found by Joost de Winter
in October 2026.
r = 2.50945+
Found by Yanis Gomes
in October 2026.
r = 2.54026+
Found by Yanis Gomes
in October 2026.


37.
           38.
           39.
r = 2.57708+
Found by Yanis Gomes
in October 2026.
r = 2.60543+
Found by Yanis Gomes
in October 2026.
r = 2.65278+
Found by Yanis Gomes
in October 2026.


40.
           41.
           42.
r = 2.68550+
Found by Yanis Gomes
in October 2026.
r = 2.71822+
Found by Yanis Gomes
in October 2026.
r = 2.74013+
Found by Yanis Gomes
in October 2026.


43.
           44.
           45.
r = 2.77805+
Found by Yanis Gomes
in October 2026.
r = √(5+2√2) = 2.79793+
Found by Yanis Gomes
in October 2026.
r = 2.83056+
Found by Joshua Wolk
in September 2026.


46.
           47.
           48.
r = 2.85425+
Found by Yanis Gomes
in October 2026.
r = 2.88442+
Found by Joost de Winter
in October 2026.
r = 2.91444+
Found by Joost de Winter
in October 2026.


49.
           50.
r = 2.93949+
Found by Joost de Winter
in October 2026.
r = 2.97772+
Found by Joost de Winter
in October 2026.