math

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??

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  1. 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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