A lissajou curve is defined by
x = cos mt, y = sin nt (0 < t < 2π),
which is smooth, if m is odd.
m = 1, n = 1
m = 1, n = 2
m = 3, n = 5
m = 5, n = 7
The rotation number
1
0
-1
1
Theorem(Y. Maezawa and H. Tsuchihashi) If m and n are positive odd numbers and
m = 1 or 3 (mod 4),
then the rotation numer is equal to 1 or -1, respectively.
Input odd numbers which are relatively prime
into the boxes below,
and then click the buttons.
m =
< 20, n =
< 20
