تعاریف طلایی تعمیم داده شده توسط ابزار

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.