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 = 3.41569+
Found by Jake Loyd
in June 2026.
           6.

s = 3.74743+
Found by Jake Loyd
in June 2026.


7.

s = 3.96756+
Found by Jake Loyd
in June 2026.
           8.

s = 4.25642+
Found by Jake Loyd
in June 2026.
           9.

s = 4.50713+
Found by Jake Loyd
in June 2026.


10.

s = 3√5–3+3√(1–2/√5) = 4.65767+
Found by Jake Loyd
in June 2026.
           11.

s = 4.86103+
Found by Jake Loyd
in June 2026.
           12.

s = 5.07519+
Found by Jake Loyd
in June 2026.


13.

s = 5.29475+
Found by Jake Loyd
in June 2026.
           14.

s = 5.49989+
Found by Jake Loyd
in June 2026.
           15.

s = 5.63035+
Found by Jake Loyd
in June 2026.


16.

s = 5.77738+
Found by Jake Loyd
in June 2026.
           17.

s = 5.92697+
Found by Jake Loyd
in June 2026.
           18.

s = 6.16318+
Found by Jake Loyd
in June 2026.


19.

s = 6.33939+
Found by Jake Loyd
in June 2026.
           20.

s = 6.45886+
Found by Jake Loyd
in June 2026.