Pursuit Curves

        The article deals with the plotting of pursuit curves and the interesting patterns they form.  One example of this is given:  “suppose that a person stands at each corner of a square traced out on the ground.  Each person looks directly at the person to his or her left, then begins to walk toward that person.  If all four people move at the same time and at the same constant speed, each person follows a spiral path toward the square’s center.”

        The article then gives directions on how to go about plotting such curves as described above (see steps 1-5 on article).

        Another interesting pattern is performed similarly but with three pursuers each starting at the corners of an equilateral triangle.  The point in the middle of the triangle at which they meet is known as a brocard point.  A brocard point has a property that lines drawn from the vertices of the point are inclined at the same angle of each side of the triangle.  This is significant because Henri Brocard found the points by studying the problem of three dogs chasing on another.  He tested using different pursuing speeds, and was able to determine that one set for each brocard point had two possible sets of spiral paths.

        Interestingly the article concludes with an artistic insight.  It claims the rules for drawing pursuit curves and their variants can serve as a media for creating artistic designs.