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Can Croatian Urban Hierarchy Be Approximated With The Fibonacci Sequence? An Analysis On Historical Population Data

Author

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  • Hrvoje Josic

    (University of Zagreb)

  • Berislav Zmuk

    (University of Zagreb)

Abstract

Fibonacci numbers can be found in nature and have application in various fields of human activity. The Fibonacci sequence can also be used to predict population of settlements. The goal of this paper is to examine whether the hierarchy of the Croatian urban system can be approximated with the Fibonacci sequence on historical census data from 1857 to 2011. Actual values of urban rank according to settlements size were compared to the predicted values using two Fibonacci methods from the Fibonacci sequence. First method divides the population of the largest city by the golden ratio constant while the second method takes the population of each successive city and divides it by the golden ratio constant. The conducted analysis has shown that Croatian urban system conforms to the Fibonacci sequence with very good precision. Method 2 gives more precise overlaps of the actual number of inhabitants by settlements in the urban hierarchy of Croatia with the Fibonacci sequence than Method 1. If the largest city Zagreb is excluded from the analysis, the estimations are more precise with smaller mean MAPE.

Suggested Citation

  • Hrvoje Josic & Berislav Zmuk, 2020. "Can Croatian Urban Hierarchy Be Approximated With The Fibonacci Sequence? An Analysis On Historical Population Data," Economic Thought and Practice, Department of Economics and Business, University of Dubrovnik, vol. 29(1), pages 3-28, june.
    • Handle: RePEc:avo:emipdu:v:29:y:2020:i:1:p:3-28
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    References listed on IDEAS

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    1. Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
    2. Ramzi Suleiman, 2017. "Economic Harmony: An Epistemic Theory of Economic Interactions," Games, MDPI, vol. 8(1), pages 1-15, January.
    3. Violeta Gaucan, 2011. "How to use Fibonacci retracement to predict forex market," Journal of Knowledge Management, Economics and Information Technology, ScientificPapers.org, vol. 1(2), pages 1-1, February.
    4. Rosen, Kenneth T. & Resnick, Mitchel, 1980. "The size distribution of cities: An examination of the Pareto law and primacy," Journal of Urban Economics, Elsevier, vol. 8(2), pages 165-186, September.
    5. William Goetzmann, 2003. "Fibonacci and the Financial Revolution," Yale School of Management Working Papers ysm432, Yale School of Management, revised 01 Mar 2004.
    6. Zora Živanović & Branka Tošić & Teodora Nikolić & Dragica Gatarić, 2019. "Urban System in Serbia—The Factor in the Planning of Balanced Regional Development," Sustainability, MDPI, vol. 11(15), pages 1-19, August.
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    More about this item

    Keywords

    Croatia; urban system; Fibonacci sequence; rank-size rule;
    All these keywords.

    JEL classification:

    • P25 - Political Economy and Comparative Economic Systems - - Socialist and Transition Economies - - - Urban, Rural, and Regional Economics
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes
    • R23 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Household Analysis - - - Regional Migration; Regional Labor Markets; Population

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