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.