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 smallest angle would be 0 with all 6 segments on top of one another.  The largest would be two of the three segments on each side over the top of the blue lines and the third between, making an equilateral triangle on both sides of the drawing.

the range is then between 0d and 60d

Posted by Carl on 2005-06-10 23:11:47