This was a cheaty sort of way of analyzing a calculus problem given to us by my teacher. We were getting nowhere using calculus, so I decided to model it and collect some data in order to give myself some additional info to go off of. The program basically replicates the bugs' motion as described in the problem, records the position of one of the bugs, and after the simulation has run its course analyzes the data collected to determine its derivative. -------------------- Problem text: Four bugs are placed at the four corners of a square with side length 'a'. The bugs crawl counterclockwise at the same speed and each bug crawls directly toward the next bug at all times. They approach the center of the square along spiral paths. Find the polar equation of a bug's path assuming the pole is at the center of the square.
