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.)

The answer is 60 degrees. If the eight points of intersection were labeled I could give you a proof. Its hard to specify an angle - do you say the angle between the red and blue lines in the lower left of the figure?

Posted by Bractals on 2005-06-09 03:53:13