Posted by **KIRA** on Wednesday, February 20, 2008 at 8:09pm.

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??

- math -
**Damon**, Wednesday, February 20, 2008 at 8:31pm
rotation matrix for rotation angle T

|cos T |-sin T|

|sin T | cos T|

That matrix, call it M

then M (column x|y) gives new x|y

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.

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