L's in Pentagons
The following pictures show n L's with short side 1 inside the smallest known pentagon (of side s).

1.

s = 1.81089+
Trivial.
  		           2.

s = 2.33322+
Trivial.
  		           3.

s = 2.79081+
Found by Jonathan Viquerat
in May 2026.

4.

s = 3.07149+
Found by Jonathan Viquerat
in May 2026. 		           5.

s = 3.50704+
Found by Jonathan Viquerat
in May 2026. 		           6.

s = 3.80457+
Found by Jonathan Viquerat
in May 2026.

7.

s = = 3.98893+
Found by Jonathan Viquerat
in May 2026. 		           8.

s = 4.29193+
Found by Jonathan Viquerat
in May 2026. 		           9.

s = 4.55142+
Found by Jonathan Viquerat
in May 2026.

10.

s = 3√5–3+3√(1–2/√5) = 4.68296+
Found by Maurizio Morandi
in May 2026. 		           11.

s = 3+√((5+√5)/2) = 4.90211+
Found by Maurizio Morandi
in May 2026. 		           12.

s = 4√5–8+13√(1–2/√5) = 5.16822+
Found by Maurizio Morandi
in May 2026.

13.

s = 3√5–2+2√(1–2/√5) = 5.35804+
Found by Maurizio Morandi
in May 2026. 		           14.

s = 5.59996+
Found by Jonathan Viquerat
in May 2026. 		           15.

s = 5.82042+
Found by Jonathan Viquerat
in May 2026.

16.

s = 4√5–4+3√(1–2/√5) = 5.91903+
Found by Maurizio Morandi
in May 2026. 		           17.

s = 3√5–2+4√(1–2/√5) = 6.00788+
Found by Maurizio Morandi
in May 2026. 		           18.

s = 6.37761+
Found by Jonathan Viquerat
in May 2026.

19.

s = 2+√5+(13/2)√(1–2/√5) = 6.34804+
Found by Maurizio Morandi
in May 2026. 		           20.

s = 3√5–6+18√(1–2/√5) = 6.55675+
Found by Maurizio Morandi
in May 2026.