Based on a simple mathematical property, a simple method is proposed f
or detecting the number of folds n contained in a given rotationally s
ymmetric shape. Skills to overcome the difficulty caused by sampling a
nd rounding errors are also discussed. Experimental results are includ
ed to show the feasibility of this new method. As for shape orientatio
n, it is just a by-product of the proposed method because no extra com
putation load is needed to get the orientation.