Symmetric uncrossed knight's paths of length <= 6
Each knight move is represented by a straight line segment of scaled length 1,
which needs to be rotated and rescaled by Sqrt(5) to fit on a chessboard.
To enable the use of Markus Sigg's Snake Viewer program, the true
direction changes of the knight's path are rounded to the nearest integer
multiples of 9 degrees. The direction changes of the path are coded by letters and 0:
0 (continuation of previous direction), d, D, f, F, j, J (right angle turn), n, N, p, P.
See the examples for lenght = 2.
The diameter of the enclosing circle of the path calculated by the drawing program
usually deviates from the indicated exact diameter due to the said mapping of the angles.
Turning angle code, diameter of enclosing circle (type of symmetry)
Length = 2 (6 paths):
p, 1.0540925534 (mirror)
j, 1.4142135624 (mirror)
f, 1.7888543820 (mirror)
0, 2.0000000000 (mirror,rot2)
D, 1.8973665961 (mirror)
N, 1.1180339887 (mirror)
Length = 3 (7 paths):
pP, 1.3416407865 (rot2)
jj, 1.4142135624 (mirror)
jJ, 2.2360679775 (rot2)
fF, 2.7202941017 (rot2)
00, 3.0000000000 (mirror,rot2)
Dd, 2.8635642127 (rot2)
Nn, 1.6124515497 (rot2)
Lenght = 4 (29 paths):
p0P, 2.0000000000 (rot2)
pFp, 1.8027756377 (mirror)
pPp, 1.4142135624 (mirror)
jfj, 1.8027756377 (mirror)
j0j, 2.2360679775 (mirror)
j0J, 2.8284271247 (rot2)
jDj, 2.5385910353 (mirror)
jJj, 2.8284271247 (mirror)
jNj, 2.6832815730 (mirror)
fdf, 2.5385910353 (mirror)
f0F, 3.5777087640 (rot2)
fFf, 3.5777087640 (mirror)
fPf, 2.5298221281 (mirror)
0p0, 2.1081851068 (mirror)
0j0, 2.8284271247 (mirror)
0f0, 3.5777087640 (mirror)
000, 4.0000000000 (mirror,rot2)
0D0, 3.7947331922 (mirror)
0N0, 2.2360679775 (mirror)
DnD, 2.6832815730 (mirror)
DdD, 3.7947331922 (mirror)
D0d, 3.7947331922 (rot2)
DFD, 2.6832815730 (mirror)
JpJ, 2.5298221281 (mirror)
JfJ, 2.6832815730 (mirror)
JDJ, 1.9436506316 (mirror)
NnN, 1.8027756377 (mirror)
NdN, 1.9436506316 (mirror)
N0n, 2.0000000000 (rot2)
Length = 5 (46 paths):
pjJP, 2.2360679775 (rot2)
pdDP, 2.8635642127 (rot2)
p00P, 3.0000000000 (rot2)
pFfP, 2.7202941017 (rot2)
pJjP, 2.2360679775 (rot2)
pPpP, 1.8439088915 (rot2)
jpPJ, 1.8439088915 (rot2)
jjJJ, 2.2360679775 (rot2)
jfFJ, 2.8635642127 (rot2)
j00j, 3.1622776602 (mirror)
j00J, 3.6055512755 (rot2)
jDdJ, 3.8209946349 (rot2)
jJjJ, 3.6055512755 (rot2)
jJJj, 3.0000000000 (mirror)
jNnJ, 3.1304951685 (rot2)
fnNF, 2.7202941017 (rot2)
fjJF, 3.2557641192 (rot2)
fdDF, 4.1231056256 (rot2)
f00F, 4.4944410108 (rot2)
fFfF, 4.4944410108 (rot2)
fJjF, 4.1231056256 (rot2)
fPpF, 3.2557641192 (rot2)
0pP0, 3.2557641192 (rot2)
0jj0, 2.2360679775 (mirror)
0jJ0, 4.1231056256 (rot2)
0fF0, 4.6690470120 (rot2)
0000, 5.0000000000 (rot2)
0Dd0, 4.8373546490 (rot2)
0Nn0, 3.4928498393 (rot2)
DnNd, 3.6055512755 (rot2)
DjJd, 4.2190046219 (rot2)
DdDd, 4.7539457296 (rot2)
D00d, 4.7539457296 (rot2)
DFfd, 4.2190046219 (rot2)
DJjd, 3.6055512755 (rot2)
DPpd, 2.8635642127 (rot2)
JpPj, 2.8635642127 (rot2)
JfFj, 3.8209946349 (rot2)
JDdj, 3.1304951685 (rot2)
JNnj, 1.8439088915 (rot2)
NnNn, 2.4083189158 (rot2)
NjJn, 2.7202941017 (rot2)
NdDn, 2.8635642127 (rot2)
N00n, 3.0000000000 (rot2)
NFfn, 2.7202941017 (rot2)
NJjn, 2.2360679775 (rot2)
Length = 6 (170 paths):
pjdjp, 1.9436506316 (mirror)
pj0JP, 2.8284271247 (rot2)
pjFjp, 2.6832815730 (mirror)
pjPjp, 2.5298221281 (mirror)
pdfdp, 2.6832815730 (mirror)
pd0DP, 3.7947331922 (rot2)
pdDdp, 3.7947331922 (mirror)
pdNdp, 2.6832815730 (mirror)
p0d0p, 3.7947331922 (mirror)
p000P, 4.0000000000 (rot2)
p0F0p, 3.5777087640 (mirror)
p0P0p, 2.1081851068 (mirror)
pFpFp, 2.5298221281 (mirror)
pFfFp, 3.5777087640 (mirror)
pF0fP, 3.5777087640 (rot2)
pFDFp, 3.1622776602 (mirror)
pJnJp, 2.6832815730 (mirror)
pJdJp, 3.1622776602 (mirror)
pJ0jP, 3.2249030993 (rot2)
pJFJp, 2.6832815730 (mirror)
pPpPp, 1.9436506316 (mirror)
pPfPp, 2.6832815730 (mirror)
pP0pP, 2.6832815730 (rot2)
jj0JJ, 2.8284271247 (rot2)
jjDjj, 2.5385910353 (mirror)
jjJjj, 2.8284271247 (mirror)
jjNjj, 2.6832815730 (mirror)
jfdfj, 2.5385910353 (mirror)
jf0FJ, 3.5777087640 (rot2)
jfFfj, 3.5777087640 (mirror)
jfPfj, 3.1622776602 (mirror)
j0j0j, 2.8284271247 (mirror)
j0f0j, 3.5777087640 (mirror)
j000j, 4.1231056256 (mirror)
j000J, 4.4721359550 (rot2)
j0D0j, 4.4271887242 (mirror)
j0J0j, 4.2426406871 (mirror)
j0N0j, 3.5777087640 (mirror)
jDnDj, 2.6832815730 (mirror)
jDdDj, 4.4271887242 (mirror)
jD0dJ, 4.8166378315 (rot2)
jDFDj, 4.4721359550 (mirror)
jJpJj, 3.1622776602 (mirror)
jJjJj, 4.2426406871 (mirror)
jJfJj, 4.4721359550 (mirror)
jJ0jJ, 4.4721359550 (rot2)
jJ0Jj, 4.0000000000 (mirror)
jJDJj, 3.1622776602 (mirror)
jNnNj, 3.5777087640 (mirror)
jNdNj, 3.1622776602 (mirror)
jN0nJ, 3.6878177829 (rot2)
fn0NF, 2.0000000000 (rot2)
fnNnf, 2.0000000000 (mirror)
fj0JF, 3.2249030993 (rot2)
fjFjf, 2.6832815730 (mirror)
fjPjf, 3.1622776602 (mirror)
fdfdf, 2.6832815730 (mirror)
fd0DF, 4.8166378315 (rot2)
fdDdf, 4.4271887242 (mirror)
fdNdf, 4.4721359550 (mirror)
f0n0f, 2.7578171722 (mirror)
f0d0f, 4.4271887242 (mirror)
f000F, 5.4405882035 (mirror)
f0F0f, 5.3665631460 (mirror)
f0P0f, 3.3429792407 (mirror)
fFpFf, 3.3429792407 (mirror)
fFfFf, 5.3665631460 (mirror)
fF0fF, 5.4405882035 (rot2)
fFDFf, 4.4271887242 (mirror)
fJnJf, 4.4721359550 (mirror)
fJdJf, 4.4271887242 (mirror)
fJ0jF, 4.8166378315 (rot2)
fJFJf, 2.5938388539 (mirror)
fPpPf, 3.1622776602 (mirror)
fPfPf, 2.5298221281 (mirror)
fP0pF, 3.2249030993 (rot2)
0p0P0, 2.6832815730 (rot2)
0pPp0, 2.4037008503 (mirror)
0j0j0, 2.8284271247 (mirror)
0j0J0, 4.4721359550 (rot2)
0jDj0, 3.3333333333 (mirror)
0jJj0, 4.2426406871 (mirror)
0jNj0, 4.4721359550 (mirror)
0fdf0, 3.3429792407 (mirror)
0f0F0, 5.4405882035 (rot2)
0fFf0, 5.3665631460 (mirror)
0fPf0, 4.4271887242 (mirror)
00p00, 3.1622776602 (mirror)
00j00, 4.2426406871 (mirror)
00f00, 5.3665631460 (mirror)
00000, 6.0000000000 (mirror,rot2)
00D00, 5.6920997883 (mirror)
00N00, 3.3541019662 (mirror)
0DnD0, 4.4721359550 (mirror)
0DdD0, 5.6920997883 (mirror)
0D0d0, 5.7271284253 (rot2)
0DFD0, 3.6671514831 (mirror)
0JpJ0, 4.4271887242 (mirror)
0JfJ0, 3.6055512755 (mirror)
0JDJ0, 2.4037008503 (mirror)
0NnN0, 2.8284271247 (mirror)
0NdN0, 2.4037008503 (mirror)
0N0n0, 3.2249030993 (rot2)
Dn0Nd, 3.6878177829 (rot2)
DnDnD, 2.6832815730 (mirror)
DnNnD, 3.5777087640 (mirror)
DjdjD, 2.6832815730 (mirror)
Dj0Jd, 4.8166378315 (rot2)
DjFjD, 4.4721359550 (mirror)
DjPjD, 4.4271887242 (mirror)
DdfdD, 4.4721359550 (mirror)
Dd0Dd, 5.7271284253 (rot2)
DdDdD, 5.6920997883 (mirror)
DdNdD, 3.6671514831 (mirror)
D0n0D, 3.6671514831 (mirror)
D0d0D, 5.6920997883 (mirror)
D000d, 5.7271284253 (rot2)
D0F0D, 4.4721359550 (mirror)
D0P0D, 2.8811863126 (mirror)
DFpFD, 4.4271887242 (mirror)
DFfFD, 4.4721359550 (mirror)
DF0fd, 4.8166378315 (rot2)
DFDFD, 2.6832815730 (mirror)
DJnJD, 3.5777087640 (mirror)
DJdJD, 2.6832815730 (mirror)
DJ0jd, 3.6878177829 (rot2)
DPpPD, 2.0000000000 (mirror)
DP0pd, 2.0000000000 (rot2)
Jp0Pj, 3.2249030993 (rot2)
JpFpJ, 2.7487370837 (mirror)
JpPpJ, 3.1622776602 (mirror)
JjfjJ, 2.7950849719 (mirror)
JjDjJ, 4.4271887242 (mirror)
JjNjJ, 3.5777087640 (mirror)
JfdfJ, 4.4271887242 (mirror)
Jf0Fj, 4.8166378315 (rot2)
JfFfJ, 4.4721359550 (mirror)
JfPfJ, 2.6201729184 (mirror)
J0p0J, 3.1622776602 (mirror)
J0f0J, 4.4721359550 (mirror)
J0D0J, 3.7947331922 (mirror)
JDnDJ, 3.5777087640 (mirror)
JDdDJ, 3.7947331922 (mirror)
JD0dj, 3.7947331922 (rot2)
JDFDJ, 2.6832815730 (mirror)
JJpJJ, 2.5385910353 (mirror)
JJfJJ, 2.6832815730 (mirror)
JN0nj, 2.0000000000 (rot2)
Nn0Nn, 3.2249030993 (rot2)
NnDnN, 3.1622776602 (mirror)
NnNnN, 2.6832815730 (mirror)
NjdjN, 3.1622776602 (mirror)
Nj0Jn, 3.6878177829 (rot2)
NjFjN, 3.5777087640 (mirror)
NjPjN, 2.5385910353 (mirror)
NdfdN, 3.5777087640 (mirror)
Nd0Dn, 3.7947331922 (rot2)
NdDdN, 3.7947331922 (mirror)
NdNdN, 2.6832815730 (mirror)
N0n0N, 2.6832815730 (mirror)
N0d0N, 3.7947331922 (mirror)
N000n, 4.0000000000 (rot2)
N0F0N, 3.5777087640 (mirror)
NFpFN, 2.5385910353 (mirror)
NFfFN, 3.5777087640 (mirror)
NF0fn, 3.5777087640 (rot2)
NFDFN, 2.5385910353 (mirror)
NJnJN, 2.6832815730 (mirror)
NJdJN, 2.5385910353 (mirror)
NJ0jn, 2.8284271247 (rot2)
Back to A323133