The following pictures show L's (with short side 1) packed inside the smallest known equilateral triangle (with side s).
1.
2.
3.
s = 2√2 + √6/3 = 3.64492+
Trivial.
s = 4 + 2/√3 = 5.15470+
Trivial.
s = 3 + 3√3/2 = 5.59807+
Found by Jonathan Viquerat
in May 2026.
4.
5.
6.
s = 6.58646+
Found by Jonathan Viquerat
in May 2026.
s = 6 + 2/√3 = 7.15470+
Found by Jonathan Viquerat
in May 2026.
s = 4 + 2√3 = 7.46410+
Found by Maurizio Morandi
in May 2026.
7.
8.
9.
s = 7 + 2/√3 = 8.15470+
Found by Jonathan Viquerat
in May 2026.
s = 8.68219+
Found by Joshua Wolk
in September 2026.
s = 5 + 7/√3 = 9.04145+
Found by Maurizio Morandi
in May 2026.
10.
11.
12.
s = 6 + 2√3 = 9.46410+
Found by Maurizio Morandi
in May 2026.
s = 4 + 10/√3 = 9.77350+
Found by Maurizio Morandi
in May 2026.
s = 10.21346+
Found by Joshua Wolk
in September 2026.
13.
14.
15.
s = 10.57224+
Found by Joshua Wolk
in September 2026.
s = 7 + 7/√3 = 11.04145+
Found by Maurizio Morandi
in May 2026.
s = 2 + 16/√3 = 11.23760+
Found by Joshua Wolk
in September 2026.
16.
17.
18.
s = 11.61625+
Found by Joshua Wolk
in September 2026.
s = 8 + 7/√3 = 12.04145+
Found by Joshua Wolk
in September 2026.
s = 12.33290+
Found by Joshua Wolk
in September 2026.
19.
20.
21.
s = 12.59796+
Found by Yanis Gomes
in October 2026.
s = 12.88164+
Found by Joshua Wolk
in September 2026.
s = 13.21674+
Found by Yanis Gomes
in October 2026.
22.
23.
24.
s = 13.49751+
Found by Joshua Wolk
in September 2026.
s = 13.75279+
Found by Yanis Gomes
in October 2026.
s = 10 + 7/√3 = 14.04145+
Found by Yanis Gomes
in October 2026.
25.
26.
27.
s = 14.35090+
Found by Yanis Gomes
in October 2026.
s = 14.61885+
Found by Yanis Gomes
in October 2026.
s = (14 + 9√3)/2 = 14.79422+
Found by Yanis Gomes
in October 2026.
28.
29.
30.
s = 7 + 14/√3 = 15.08290+
Found by Maurizio Morandi
in October 2026.
s = 9 + 11/√3 = 15.35085+
Found by Maurizio Morandi
in October 2026.
s = 4 + 20/√3 = 15.54700+
Found by Yanis Gomes
in October 2026.
31.
32.
33.
s = 10(1 + 1/√3) = 15.77350+
Found by Maurizio Morandi
in November 2026.
s = 16.08294+
Found by Yanis Gomes
in October 2026.
s = (21+16√3)/3 = 16.23760+
Found by Yanis Gomes
in October 2026.
34.
35.
36.
s = 13 + 2√3 = 16.46410+
Found by Maurizio Morandi
in October 2026.
s = 4 + 22/√3 = 16.70170+
Found by Maurizio Morandi
in October 2026.
s = 10 + 4√3 = 16.92820+
Found by Maurizio Morandi
in October 2026.
37.
38.
39.
s = 16 + 2/√3 = 17.15470+
Found by Maurizio Morandi
in October 2026.
s = 7 + 6√3 = 17.39230+
Found by Maurizio Morandi
in October 2026.
s = 17.61701+
Found by Yanis Gomes
in October 2026.
40.
41.
42.
s = 4 + 8√3 = 17.85640+
Found by Maurizio Morandi
in October 2026.
s = 14 + 7/√3 = 18.04145+
Found by Maurizio Morandi
in October 2026.
s = 13 + 3√3 = 18.19615+
Found by Maurizio Morandi
in October 2026.
43.
44.
45.
s = 15 + 2√3 = 18.46410+
Found by Maurizio Morandi
in October 2026.
s = 14 + 8/√3 = 18.61880+
Found by Maurizio Morandi
in October 2026.
s = 13 + 10/√3 = 18.77350+
Found by Maurizio Morandi
in October 2026.
46.
47.
48.
s = 4 + 26/√3 = 19.01110+
Found by Maurizio Morandi
in October 2026.
s = 17 + 4/√3 = 19.30940+
Found by Maurizio Morandi
in October 2026.
s = 5 + 25/√3 = 19.43375+
Found by Maurizio Morandi
in October 2026.
49.
50.
s = 15 + 8/√3 = 19.61880+
Found by Maurizio Morandi
in November 2026.
s = 2√2 + √6/3 + 28/√3 = 19.81073+
Found by Maurizio Morandi
in October 2026.