# Rooted uncrossed knight's paths of length <= 3

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.

Isomorphisms by reflection and path reversal are indicated by (same as ...)

#### Turning angle code, diameter of enclosing circle (symmetry)

#### Length = 2 (7 paths):

p, 1.0540925534 (symmetric)

j, 1.4142135624 (symmetric)

f, 1.7888543820 (symmetric)

0, 2.0000000000 (symmetric)

D, 1.8973665961 (symmetric)

J, 1.4142135624 (symmetric) (same as j)

N, 1.1180339887 (symmetric)

#### Length = 3 (47 paths):

pj, 1.4142135624

pd, 1.8973665961

p0, 2.0000000000

pF, 1.8027756377

pJ, 1.6288220359

pP, 1.3416407865 (symmetric)

jp, 1.4142135624 (same as pj)

jj, 1.4142135624 (symmetric)

jf, 1.8027756377

j0, 2.2360679775

jD, 2.4083189158

jJ, 2.2360679775 (symmetric)

jN, 1.8439088915

fn, 1.7888543820

fj, 1.8027756377 (same as jf)

fd, 2.4083189158

f0, 2.7202941017

fF, 2.7202941017 (symmetric)

fJ, 2.4083189158

fP, 1.8027756377 (same as pF)

0p, 2.0000000000 (same as p0)

0j, 2.2360679775 (same as j0)

0f, 2.7202941017 (same as f0)

00, 3.0000000000 (symmetric)

0D, 2.8635642127

0J, 2.2360679775 (same as j0)

0N, 2.0000000000

Dn, 1.9436506316

Dj, 2.4083189158 (same as jD)

Dd, 2.8635642127 (symmetric)

D0, 2.8635642127 (same as 0D)

DF, 2.4083189158 (same as fd)

DJ, 1.9436506316

DP, 1.8973665961 (same as pd)

Jp, 1.6288220359 (same as pJ)

Jj, 2.2360679775 (symmetric) (same as jJ)

Jf, 2.4083189158 (same as fJ)

J0, 2.2360679775 (same as j0)

JD, 1.9436506316 (same as DJ)

JJ, 1.4142135624 (symmetric) (same as jj)

JN, 1.4142135624

Nn, 1.6124515497 (symmetric)

Nj, 1.8439088915 (same as jN)

Nd, 1.9436506316 (same as Dn)

N0, 2.0000000000 (same as 0N)

NF, 1.7888543820 (same as fn)

NJ, 1.4142135624 (same as JN)

Back to A323131