math
posted by KIRA on .
how can you determine whether a design has rotational symmetry? if a design has a rotational symmetry, how many can you find the angle of roation??

rotation matrix for rotation angle T
cos T sin T
sin T  cos T
That matrix, call it M
then M (column xy) gives new xy
for example if T = 90 degrees
 0 1  [x]
 1  0  [y]
gives
0 x  y = y for new x value
and
1 x + 0 y = x for new y value
SO you can reverse that
new x = old x cos T  old y sin T
new y = old x sin T + old y cos T
If you have a bunch of old x and y values and their corresponding new values, you can solve for sin T and Cos T and therefore for T, the rotation angle.