In the picture all of the red segments are of equal length and all of their endpoints lie on one of the two blue lines. Determine all possible values for the smaller angle between the blue lines.

(This problem is a special case of a problem discovered by Daniel Shapiro, professor of mathematics at Ohio State University. His problem generalizes a problem he saw years ago.)

(In reply to Solution by Carl)

Caught in the symmetry trap.  The range is 0d to 90d

0d as noted before.  90d can be made by making two equilateral triangles on one side of the blue cross, then sliding it towards the center (it won't be a triangle anymore, but a trianble with whiskers), until the blue lines are at right angles.

Posted by Carl on 2005-06-10 23:24:29