Squares in Tans

Squares in Tans
The following pictures show n squares with side 1 packed inside the smallest known tan (of leg length s ).

1.
2.
3.

s = 2
Trivial. s = 2√2 = 2.828+
Trivial. s = 3
Trivial.

4.
5.
6.

s = 5 / √2 = 3.535
Found by Erich Friedman
in March 2005. s = 4
Found by Erich Friedman
in March 2005. s = 4
Trivial.

7.
8.
9.

s = 3 + √2 = 4.414+
Found by Erich Friedman
in March 2005. s = 2 + 2√2 = 4.828+
Found by Erich Friedman
in March 2005. s = 7 / √2 = 4.949+
Found by Erich Friedman
in March 2005.

10.
11.
12.

s = 5
Trivial. s = 4 + √2 = 5.414+
Found by Erich Friedman
in March 2005. s = 4√2 = 5.656+
Found by Erich Friedman
in March 2005.

13.
14.
15.

s = 3 + 2√2 = 5.828+
Found by Erich Friedman
in March 2005. s = 6
Found by Erich Friedman
in March 2005. s = 6
Trivial.

16.
17.
18.

s = 9 / √2 = 6.363+
Found by Erich Friedman
in March 2005. s = 5 + √2 = 6.414+
Found by Erich Friedman
in March 2005. s = 4 + 2√2 = 6.828+
Found by Erich Friedman
in March 2005.

19.
20.
21.

s = 2 + 7 / √2 = 6.949+
Found by David W. Cantrell
in May 2005. s = 7
Found by Erich Friedman
in March 2005. s = 7
Trivial.

22.
23.
24.

s = 1 + 9 / √2 = 7.363+
Found by Erich Friedman
in March 2005. s = 6 + √2 = 7.414+
Found by Erich Friedman
in March 2005. s = 7 + 1 / √2 = 7.707+
Found by David W. Cantrell
in May 2005.

25.		26.		27.-28.
s = 11 / √2 = 7.778+ Trivial.		s = 5 + 2√2 = 7.828+ Found by Erich Friedman in March 2026.		s = 8 Trivial.

29.		30.		31.
s = 8.36396+ Found by Joshua Wolk in September 2026.		s = 7 + √2 = 8.41421+ Found by Joshua Wolk in September 2026.		s = 8.48528+ Found by Joshua Wolk in September 2026.

32.		33.		34.
s = 8.77817+ Found by Joshua Wolk in September 2026.		s = 6 + 2√2 = 8.82842+ Found by Yanis Gomes in October 2026.		s = 4 + 7/√2 = 8.94974+ Found by Yanis Gomes in October 2026.

35.-36.		37.		38.-39.
s = 9 Trivial.		s = 9.24264+ Found by Joshua Wolk in September 2026.		s = 8 + √2 = 9.41421+ Found by Joshua Wolk in September 2026.

40.		41.-42.		43.
s = 9.77817+ Found by Joshua Wolk in September 2026.		s = 7 + 2√2 = 9.82842+ Found by Yanis Gomes in October 2026.		s = 9.89949+ Found by Joshua Wolk in September 2026.

44.-45.		46.		47.-48.
s = 10 Trivial.		s = 10.24264+ Found by Joshua Wolk in September 2026.		s = 9 + √2 = 10.41421+ Found by Joshua Wolk in September 2026.

49.		50.
s = 10.60660+ Found by Joshua Wolk in September 2026.		s = 10.65685+ Found by Oihan Barreneche in October 2026.

1.		2.		3.
s = 2 Trivial.		s = 2√2 = 2.828+ Trivial.		s = 3 Trivial.

4.		5.		6.
s = 5 / √2 = 3.535 Found by Erich Friedman in March 2005.		s = 4 Found by Erich Friedman in March 2005.		s = 4 Trivial.

7.		8.		9.
s = 3 + √2 = 4.414+ Found by Erich Friedman in March 2005.		s = 2 + 2√2 = 4.828+ Found by Erich Friedman in March 2005.		s = 7 / √2 = 4.949+ Found by Erich Friedman in March 2005.

10.		11.		12.
s = 5 Trivial.		s = 4 + √2 = 5.414+ Found by Erich Friedman in March 2005.		s = 4√2 = 5.656+ Found by Erich Friedman in March 2005.

13.		14.		15.
s = 3 + 2√2 = 5.828+ Found by Erich Friedman in March 2005.		s = 6 Found by Erich Friedman in March 2005.		s = 6 Trivial.

16.		17.		18.
s = 9 / √2 = 6.363+ Found by Erich Friedman in March 2005.		s = 5 + √2 = 6.414+ Found by Erich Friedman in March 2005.		s = 4 + 2√2 = 6.828+ Found by Erich Friedman in March 2005.

19.		20.		21.
s = 2 + 7 / √2 = 6.949+ Found by David W. Cantrell in May 2005.		s = 7 Found by Erich Friedman in March 2005.		s = 7 Trivial.

22.		23.		24.
s = 1 + 9 / √2 = 7.363+ Found by Erich Friedman in March 2005.		s = 6 + √2 = 7.414+ Found by Erich Friedman in March 2005.		s = 7 + 1 / √2 = 7.707+ Found by David W. Cantrell in May 2005.