Originally posted by talzamir
Christmas is coming, and one of the ornaments I see here often looks like a nine-pointed star, a nonagram. How wide is the angle at the sharp points?
One can visualize two circles; one that intersects the "outer (so called sharp) points" and one that intersects the "inner" points (the points near the center, between the outer points). Each circle has a radius; call them ro and ri. The inner circle radius can approach zero as a minimum, and can approach ro as its maximum (beyond this maximum, the inner points become outer points). It does not seem to me to be possible that the angle the puzzle asks for is some specific value; it is a function of ri/ro. Maybe the puzzle is to define this function.
At the limit of ri=0, the angle of the sharp outer points is zero (9 line segments radiating from a center) and the angle of each "sharp" inner point is 360/9 = 40 degrees.
At the limit of ri=ro, we have an 18-sided regular polygon with a rather unsharp interior angle of 160 degrees. (http://www.mathopenref.com/polygoninteriorangles.html)
That's as far as I am going with this before someone weighs in on my thinking.