3.27 Circular city, revisited Suppose that two points (R_{1}, _{2}) and (R_{2}, _{2}) are independently, uniformly distributed over a circular city of radius r_{o} and area A= Suppose further that this city has a large number of radial routes and circular ring routes so that the travel distance between (R_{1}, _{1}) and (R_{2}, _{2}) can be accurately approximated as D = R1  R2 + Min [ R1, R2] _{1}  _{2} where 0 _{1}  _{2} signifies the magnitude of the angular difference between _{1} and _{2}. In words, travel from an outer point, say, (R_{1},_{1}) if R, > R2, to an inner point (R_{2},_{1}) first occurs along a radial route to a ring located a distance R2 from the city center, and then along that ring (in the direction of minimum travel distance) to (R_{2},_{1}); the same path is traveled in reverse if travel is from (R_{2},_{1}) to (R_{1},_{1}). A sample path is shown in Figure P3.27.
