Unrooted uncrossed knight's paths of length <= 4
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 (symmetry)
Length = 2 (6 paths):
p, 1.0540925534 (symmetric)
j, 1.4142135624 (symmetric)
f, 1.7888543820 (symmetric)
0, 2.0000000000 (symmetric)
D, 1.8973665961 (symmetric)
N, 1.1180339887 (symmetric)
Length = 3 (25 paths):
pj, 1.4142135624
pd, 1.8973665961
p0, 2.0000000000
pF, 1.8027756377
pJ, 1.6288220359
pP, 1.3416407865 (symmetric)
jj, 1.4142135624 (symmetric)
jf, 1.8027756377
j0, 2.2360679775
jD, 2.4083189158
jJ, 2.2360679775 (symmetric)
jN, 1.8439088915
fn, 1.7888543820
fd, 2.4083189158
f0, 2.7202941017
fF, 2.7202941017 (symmetric)
fJ, 2.4083189158
00, 3.0000000000 (symmetric)
0D, 2.8635642127
0N, 2.0000000000
Dn, 1.9436506316
Dd, 2.8635642127 (symmetric)
DJ, 1.9436506316
JN, 1.4142135624
Nn, 1.6124515497 (symmetric)
Length = 4 (160 paths):
pjn, 1.4142135624
pjj, 1.4142135624
pjd, 1.9436506316
pj0, 2.2360679775
pjF, 2.4083189158
pjJ, 2.2360679775
pjP, 1.6288220359
pdj, 1.9436506316
pdf, 2.4083189158
pd0, 2.8635642127
pdD, 2.8635642127
pdJ, 2.4083189158
pdN, 1.9436506316
p0n, 2.0000000000
p0j, 2.2360679775
p0d, 2.8635642127
p00, 3.0000000000
p0F, 2.7202941017
p0J, 2.2360679775
p0P, 2.0000000000 (symmetric)
pFp, 1.8027756377 (symmetric)
pFj, 2.4083189158
pFf, 2.7202941017
pF0, 2.7283304386
pFD, 2.5385910353
pFJ, 2.0000000000
pFN, 1.8027756377
pJn, 1.8439088915
pJj, 2.2360679775
pJd, 2.5385910353
pJ0, 2.6076809621
pJF, 2.2803508502
pJJ, 1.8027756377
pPp, 1.4142135624 (symmetric)
pPj, 2.0000000000
pPf, 2.2803508502
pP0, 2.2803508502
pPD, 2.0000000000
pPJ, 1.4142135624
jpF, 1.8027756377
jpJ, 1.6288220359
jjf, 1.8027756377
jj0, 2.2360679775
jjD, 2.4083189158
jjJ, 2.2360679775
jjN, 1.9436506316
jfn, 1.8027756377
jfj, 1.8027756377 (symmetric)
jfd, 2.4083189158
jf0, 2.7202941017
jfF, 2.7283304386
jfJ, 2.5385910353
j0j, 2.2360679775 (symmetric)
j0f, 2.7283304386
j00, 3.1622776602
j0D, 3.2249030993
j0J, 2.8284271247 (symmetric)
j0N, 2.3177361425
jDn, 2.4083189158
jDj, 2.5385910353 (symmetric)
jDd, 3.2249030993
jD0, 3.4058772732
jDF, 3.1622776602
jDJ, 2.6832815730
jJj, 2.8284271247 (symmetric)
jJf, 3.1622776602
jJ0, 3.1622776602
jJD, 2.8284271247
jJN, 2.2360679775
jNn, 2.2803508502
jNj, 2.6832815730 (symmetric)
jNd, 2.8284271247
jN0, 2.6076809621
jNF, 2.0000000000
jNJ, 1.8439088915
fn0, 2.0000000000
fnD, 2.0000000000
fnN, 2.0000000000
fjn, 1.8027756377
fjd, 2.0000000000
fj0, 2.2360679775
fjF, 2.5385910353
fjJ, 2.6076809621
fdj, 2.4083189158
fdf, 2.5385910353 (symmetric)
fd0, 3.2249030993
fdD, 3.4058772732
fdN, 2.6832815730
f0n, 2.7202941017
f0d, 3.4058772732
f00, 3.6878177829
f0F, 3.5777087640 (symmetric)
f0J, 3.1622776602
fFj, 3.1622776602
fFf, 3.5777087640 (symmetric)
fF0, 3.6878177829
fFD, 3.4058772732
fFN, 2.7202941017
fJn, 2.6832815730
fJd, 3.4058772732
fJ0, 3.2249030993
fJJ, 2.4083189158
fPj, 2.6076809621
fPf, 2.5298221281 (symmetric)
fP0, 2.2360679775
fPD, 2.0000000000
0pd, 2.0000000000
0p0, 2.1081851068 (symmetric)
0pJ, 2.3035022138
0j0, 2.8284271247 (symmetric)
0jD, 3.1622776602
0jN, 2.8284271247
0fn, 2.7202941017
0fd, 3.1622776602
0f0, 3.5777087640 (symmetric)
0fJ, 3.4058772732
000, 4.0000000000 (symmetric)
00D, 3.8470768123
00N, 3.0000000000
0Dn, 2.8926366759
0Dd, 3.8470768123
0D0, 3.7947331922 (symmetric)
0DJ, 2.8635642127
0JD, 2.4037008503
0JN, 2.2360679775
0Nn, 2.5298221281
0Nd, 2.4037008503
0N0, 2.2360679775 (symmetric)
0NJ, 2.0000000000
Dnj, 1.9436506316
DnD, 2.6832815730 (symmetric)
DnN, 2.6076809621
Djn, 2.4083189158
Djd, 2.6832815730
DjJ, 3.2249030993
Ddj, 2.8926366759
DdD, 3.7947331922 (symmetric)
DdN, 2.8635642127
D0n, 2.8635642127
D0d, 3.7947331922 (symmetric)
D0J, 2.8926366759
DFj, 3.2249030993
DFD, 2.6832815730 (symmetric)
DFN, 2.4083189158
DJn, 2.6076809621
DJJ, 1.9436506316
DPj, 2.0000000000
JpJ, 2.5298221281 (symmetric)
JjN, 2.3177361425
Jfn, 2.4083189158
JfJ, 2.6832815730 (symmetric)
J0N, 2.2360679775
JDn, 2.2803508502
JDJ, 1.9436506316 (symmetric)
JJN, 1.4142135624
JNn, 1.6288220359
NnN, 1.8027756377 (symmetric)
Njn, 1.8439088915
NdN, 1.9436506316 (symmetric)
N0n, 2.0000000000 (symmetric)
Back to A323132