The following pictures show n unit circles packed inside the smallest known tan (of leg length s).

1.
2.
3.
s = 2 + √2 = 3.414+

Trivial.
s = 2 + 2√2 = 4.828+

Proved by Yinfeng Xu

in 1996.
s = 4 + √2 = 5.414+

Proved by Yinfeng Xu

in 1996.

4.
5.
6.
s = 2 + 3√2 = 6.242+

Proved by Yinfeng Xu

in 1996.
s = 4 + √2 + √3 = 7.146+

Proved by Hans Melissen

in 1997.
s = 6 + √2 = 7.414+

Proved by Hans Melissen

in 1997.

7.
8.
9.
s = 8.181+

Proved by Yinfeng Xu

in 1996.
s = 2 + 3√2 + √6 = 8.692+

Found by Hans Melissen

in 1997.
s = 2 + 5√2 = 9.071+

Trivial.

10.
11.
12.
s = 8 + √2 = 9.414+

Trivial.
s = 5 + √(2/3) + 3√2 = 10.059+

Found by David W. Cantrell

in June 2005.
s = 10.422+

Found by David W. Cantrell

in June 2005.

13.
14.
15.
s = 10.798+

Found by Hans Melissen

in 1997.
s = 2 + 3√2 + 2√6 = 11.141+

Found by Erich Friedman

in April 2005.
s = 10 + √2 = 11.414+

Trivial.

16.
17.
18.
s = 11.892+

Found by David W. Cantrell

in January 2006.
s = 12.155+

Found by David W. Cantrell

in January 2006.
s = 12.542+

Found by Eckard Specht

in April 2009.

19.
20.
21.
s = 12.798+

Found by David W. Cantrell

in January 2006.
s = 13.092+

Found by Maurizio Morandi

in December 2008.
s = 12 + √2 = 13.414+

Trivial.