Self-avoiding paths of maximum length
and minimum diameter on the square lattice
Number of segments, diameter of enclosing circle, squared radius of e.c.
4 1.4142135624 1/2
6 2.2360679775 5/4
8 2.8284271247 2
12 3.1622776602 5/2
14 3.8005847503 65/18
15 4.1231056256 17/4
16 4.2426406871 9/2
18 4.4721359550 5
20 4.8083261121 289/50
21 5.0000000000 25/4
23 5.0990195136 13/2
24 5.2704627669 125/18
25 5.3851648071 29/4
26 5.4918120871 377/50
27 5.5901699437 125/16
28 5.7008771255 65/8
32 5.830951894845 17/2
34 6.403124237433 41/4
36 6.529931086926 533/50
38 6.708203932499 45/4
40 6.896375859827 1189/100
44 7.071067811865 25/2
46 7.388597175901 29725/2178
48 7.475128829686 1369/98
52 7.615773105864 29/2
56 8.062257748299 65/4
58 8.310385069297 1105/64
60 8.498365855988 325/18
Back to A346124.