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Applications of Taxicab Geometry We will consider three real life situations proposed in Eugene F. Krause's book, Taxicab Geometry. First, a dispatcher for Ideal City Police Department receives a report of an accident at X = (-1,4). There are two police cars located in the area. Car C is at (2,1) and car D is at (-1,-1). Which car should be sent? Second, there are three high schools in Ideal city. Roosevelt at (2,1), Franklin at ( -3,-3) and Jefferson at (-6,-1). Draw in school district boundaries so that each student in Ideal City attends the school closet to them. For the third problem a telephone company wants to set up payphone booths so that everyone living with in twelve blocks of the center of town is with in four blocks of a payphone. Money is tight, the phone company wants to put in the least amount of payphones possible such that this is true. These examples illustrate the many uses that taxicab geometry has on the real world. We will sketch a solution to Problem 1. The police cars cannot drive through peoples' houses. They have to stick to the streets. Taxicab geometry will be the best choice to solve this problem. One simply needs to compare the distance in taxicab geometry from the dispatche r to each patrol car. The distance between accident X and car C is: d(X,C) = [(-1,4),(2,1)] = 3 + 3 = 6, by definition of taxicab distance. The distance between accident X and car D is: d(X,D) = [(-1,4),(-1,-1)] = 0 + 5 = 5. Thus we can clearly see that car D is one block closer to accident X. |
