alt Hacker NewsI'm wary of asking questions (my curiosity is bounded), but what changes if you limit the range of allowed angles to multiples of, say, 10°? How about 90°, does pi go away then?
I'm wary of asking questions (my curiosity is bounded), but what changes if you limit the range of allowed angles to multiples of, say, 10°? How about 90°, does pi go away then?
Author here. If I understand the question, the answer is that the average number of lines that the "noodle" intersects depends only on the length of the noodle. If you change the angles between the segments, the average stays the same.
So taking the limit of a large number of segments converging to a circle of diameter W leads to the result that the average number of intersections must be 2L/\pi.