Consider the graph of r= theta for theta > 0 given in radians, also known as the Archimedean spiral. Prove that the intersections of this graph with any ray whose initial point is the origin are equidistant from each other. What is that distance?
Here's the picture of a few of these intersection points for a particular ray:
Note that we aren't including the origin as one of the intersections in the picture, since we aren't including the origin in the graph!