Definition of the metropolitan area by rank-size rule (Case Study: Arak City)

The urban areas put the cities in special geographical spaces and research about these urban areas and definition of its boundary is a new field for urban studies. The metropolitan areas has included central city and population and production centers and other services that they put with another in environmental, economic, social and special contacts and they make an unique system of residence and action for now and future. The management of this areas has been ended by an unique and well system. The metropolitan area as an operational and correlative area has a regular pattern for social and population relations. The Arak city joined many huge sections and boundaries to itself from 1389 year by sanction of high council of urban planning and architecture. In this study, the researcher by presentation of standards and metroploitan patterns in Iran and by help of rank-size rule find out that this city has the capacity for urban concentration with comparison to Shazand, Toure, Mohajeran, Javersian, Davoud Abad and Karchan at the radius of 45 km. Also, Saveh City based on the research has the minimum population that it makes the relations with the other cities for central city week and by short distance with the other cities. So, we can definite an metropolitan area for this region of province.