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Generalized Golden Ratios defined by means

Author

Listed:
  • Crăciun, Ioana
  • Inoan, Daniela
  • Popa, Dorian
  • Tudose, Lucian

Abstract

Golden Ratio is defined by a proportion corresponding to the geometric mean. We introduce a generalized Golden Ratio as a fixed point of an operator defined by an arbitrary mean satisfying certain conditions. An algorithm for the evaluation of the generalized Golden Ratio is obtained using Banach’s fixed point theorem. As applications we show that some problems in shape optimization correspond to some aesthetic standards introduced in the paper.

Suggested Citation

  • Crăciun, Ioana & Inoan, Daniela & Popa, Dorian & Tudose, Lucian, 2015. "Generalized Golden Ratios defined by means," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 221-227.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:221-227
    DOI: 10.1016/j.amc.2014.10.095
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    References listed on IDEAS

    as
    1. Stakhov, A.P., 2005. "The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 263-289.
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