Octagons in Pentagons
The following pictures show n unit octagons inside the smallest known pentagon (of side s).

1.

s = 1.87981+
Trivial.
  		           2.

s = 3.35605+
Found by Jonathan Viquerat
in May 2026. 		           3.

s = 3.74411+
Found by Bhavithran Ananthan
in May 2026.

4.

s = 4.10125+
Found by Bhavithran Ananthan
in July 2026. 		           5.

s = 4.33300+
Found by Jonathan Viquerat
in May 2026. 		           6.

s = 4.77007+
Found by Jonathan Viquerat
in May 2026.

7.

s = = 5.25544+
Found by Jonathan Viquerat
in May 2026. 		           8.

s = 5.61662+
Found by Jonathan Viquerat
in May 2026. 		           9.

s = 5.96580+
Found by Jonathan Viquerat
in May 2026.

10.

s = 6.28146+
Found by Jonathan Viquerat
in May 2026. 		           11.

s = 6.46576+
Found by Jonathan Viquerat
in May 2026. 		           12.

s = 6.71763+
Found by Jonathan Viquerat
in May 2026.

13.

s = 6.97061+
Found by Aapo Lipponen
in July 2026. 		           14.

s = 7.16083+
Found by Jonathan Viquerat
in May 2026. 		           15.

s = 7.36431+
Found by Jonathan Viquerat
in May 2026.

16.

s = 7.61505+
Found by Bhavithran Ananthan
in June 2026. 		           17.

s = 7.91419+
Found by Bhavithran Ananthan
in July 2026. 		           18.

s = 8.12567+
Found by Bhavithran Ananthan
in June 2026.

19.

s = 8.34354+
Found by Bhavithran Ananthan
in July 2026. 		           20.

s = 8.54202+
Found by Bhavithran Ananthan
in July 2026. 		           21.

s = 8.74315+
Found by Jonathan Viquerat
in August 2026.

22.

s = 8.96230+
Found by Jonathan Viquerat
in August 2026. 		           23.

s = 9.11759+
Found by Jonathan Viquerat
in August 2026. 		           24.

s = 9.27759+
Found by Joshua Wolk
in September 2026.

25.

s = 9.45135+
Found by Jonathan Viquerat
in August 2026. 		           26.

s = 9.62580+
Found by Joshua Wolk
in September 2026. 		           27.

s = 9.79311+
Found by Joshua Wolk
in September 2026.

28.

s = 9.97086+
Found by Joshua Wolk
in September 2026. 		           29.

s = 10.10396+
Found by Joshua Wolk
in September 2026. 		           30.

s = 10.23777+
Found by Joshua Wolk
in September 2026.

31.

s = 10.47773+
Found by Joshua Wolk
in September 2026. 		           32.

s = 10.66882+
Found by Joshua Wolk
in September 2026. 		           33.

s = 10.81245+
Found by Joshua Wolk
in September 2026.

34.

s = 10.96020+
Found by Joshua Wolk
in September 2026. 		           36.

s = 11.14162+
Found by Joshua Wolk
in September 2026. 		           36.

s = 11.28693+
Found by Joshua Wolk
in September 2026.

37.

s = 11.42684+
Found by Joshua Wolk
in September 2026. 		           38.

s = 11.56403+
Found by Joshua Wolk
in September 2026. 		           39.

s = 11.65903+
Found by Joshua Wolk
in September 2026.

40.

s = 11.82143+
Found by Joshua Wolk
in September 2026. 		           41.

s = 11.94914+
Found by Joshua Wolk
in September 2026. 		           42.

s = 12.08789+
Found by Joshua Wolk
in September 2026.

43.

s = 12.22885+
Found by Joshua Wolk
in September 2026. 		           44.

s = 12.38287+
Found by Joshua Wolk
in September 2026. 		           45.

s = 12.50698+
Found by Joshua Wolk
in September 2026.

46.

s = 12.65087+
Found by Joshua Wolk
in September 2026. 		           47.

s = 12.76143+
Found by Joshua Wolk
in September 2026. 		           48.

s = 12.86605+
Found by Joshua Wolk
in September 2026.

49.

s = 13.02555+
Found by Joshua Wolk
in September 2026. 		           50.

s = 13.11122+
Found by Joshua Wolk
in September 2026.