The following pictures show n tans with leg 1 packed inside the smallest known squares (of side s ).
1.
2.
3.-4.
s = 1
Trivial.
s = 1
Trivial.
s = √2 = 1.414+
Trivial.
5.
6.
7.
s = 1.788+
Found by Maurizio Morandi
in August 2007.
s = 1.937+
Found by Maurizio Morandi
in February 2008.
s = 1.999+
Found by Maurizio Morandi
in August 2007.
8.
9.
10.
s = 2
Trivial.
s = 3/2 + 1/√2 = 2.207+
Found by Erich Friedman
in March 2005.
s = 2.39057+
Found by Joshua Wolk
in September 2026.
11.
12.
13.
s = 1 + √2 = 2.414+
Found by Maurizio Morandi
in August 2007.
s = 2.61005+
Found by Joshua Wolk
in September 2026.
s = 2.688+
Found by Maurizio Morandi
in March 2008.
14.
15.
16.
s = 2.76246+
Found by Joshua Wolk
in September 2026.
s = 2.82714+
Found by Joshua Wolk
in September 2026.
s = 2√2 = 2.828+
Trivial.
17.
18.
19.
s = 2.970+
Found by David W. Cantrell
in August 2007.
s = 3
Trivial.
s = 3.19001+
Found by Joshua Wolk
in September 2026.
20.
21.
22.
s = 3.26733+
Found by Joshua Wolk
in September 2026.
s = 3.340+
Found by Maurizio Morandi
in March 2008.
s = 3.392+
Found by Maurizio Morandi
in December 2007.
23.
24.
25.
s = 3.46363+
Found by Joshua Wolk
in September 2026.
s = 3.51127+
Found by Joshua Wolk
in September 2026.
s = 3.62132+
Found by Joshua Wolk
in September 2026.
26.
27.
28.
s = 3.70636+
Found by Joshua Wolk
in September 2026.
s = 3.77960+
Found by Joshua Wolk
in September 2026.
s = 3.82665+
Found by Yanis Gomes
in October 2026.
29.
30.
31.
s = 3.89517+
Found by Yanis Gomes
in October 2026.
s = 3.91421+
Found by Joost de Winter
in October 2026.
s = 3.99812+
Found by Joshua Wolk
in September 2026.
32.
33.
34.
s = 4
Trivial.
s = 4.11315+
Found by Joshua Wolk
in September 2026.
s = 4.18134+
Found by Joost de Winter
in October 2026.
35.
36.
37.
s = 4.24248+
Found by Yanis Gomes
in October 2026.
s = 3√2 = 4.24264+
Trivial.
s = 3/2 + 2√2 = 4.32842+
Found by Maurizio Morandi
in October 2026.
38.
39.
40.
s = 4.39753+
Found by Joshua Wolk
in September 2026.
s = 4.48598+
Found by Joshua Wolk
in September 2026.
s = 4.53524+
Found by Joost de Winter
in October 2026.
41.
42.
43.
s = 4.61969+
Found by Joshua Wolk
in September 2026.
s = (6+9√2)/4 = 4.68198+
Found by Maurizio Morandi
in October 2026.
s = 4.73137+
Found by Joshua Wolk
in September 2026.
44.
45.
46.
s = 3 + 5√2/4 = 4.76776+
Found by Maurizio Morandi
in October 2026.
s = 2 + 2√2 = 4.82842+
Found by Maurizio Morandi
in October 2026.
s = 4.88118+
Found by Yanis Gomes
in October 2026.
47.
48.
49.
s = 4.92727+
Found by Joshua Wolk
in September 2026.
s = 7/√2 = 4.94974+
Found by Joshua Wolk
in September 2026.
s = 4.98296+
Found by Joshua Wolk
in September 2026.
50.
s = 5
Trivial.