Generalized Golden Ratios defined by means

Ioana Crăciun, Daniela Inoan, Dorian Popa and Lucian Tudose

Applied Mathematics and Computation, 2015, vol. 250, issue C, 221-227

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.

Keywords: Golden Ratio; Homogeneous mean; Power mean; Banach’s fixed point theorem (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:250:y:2015:i:c:p:221-227

DOI: 10.1016/j.amc.2014.10.095

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