Math Problem                                                                                

                                                                                                                                           

       Imagine a map of a network of roads. Some roads end in dead ends. There are lots of enclosed areas. Suppose that you want to pick a random point on any road. You could convert the many lines representing the roads into one long line and then pick a random point on the long line and then convert back to see where the point is (where and on what road). 

 

       Supose that you make a dart board and throw a dart at the map. Suppose you make sure that you hit a road. Imagine mountains that rise up steeply from the edges of the roads to guide the dart down to a road. Then no matter where you throw the dart, you always hit a line. The steep sides of the mountains guide the dart down to a line.  What is the math to do this?  

 

 

 

 

 

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