Applying the concept of fuzzy logic (an abstract version of Boolean logic) to well-known algorithms generates an abstract version (i.e., fuzzy algorithm) that often results in computational improvements. Precision may be reduced but counteracted by gaining computational efficiency. The trade-offs (e.g., small increase in space, loss of precision) for a variety of applications are deemed accepta...

The number (1 + √ 5)/2 = 1.618 … is widely known as the golden ratio, φ and phi. Phi appears in many different equations and formulas and has many interesting properties. Many people have heard marvelous tales about phi and how it permeates art and nature. My first exposure to phi was in a comic book entitled Donald in Mathmagic Land, which later became an animated cartoon seen by millions of p...

In this article, a class of convergent series based on Fibonacci sequence is introduced for which there is a golden ratio (i.e. $frac{1+sqrt 5}{2}),$ with respect to convergence analysis. A class of sequences are at first built using two consecutive numbers of Fibonacci sequence and, therefore,  new sequences have been used in order  to introduce a  new class of series. All properties of the se...

optimization of the exploitation operation is one of the most important issues facing the mining engineers. since several technical and economic parameters depend on the cut-off grade, optimization of this parameter is of particular importance. the aim of this optimization is to maximize the net present value (npv). since the objective function of this problem is non-linear, three methods can b...

By defining the non-adjacent number, p(G, k), and topological index, ZG, for a graph G, several sequences of graphs are shown to be closely related to the golden ratio, τ. Namely, the Z-values of the path and cycle graphs are Fibonacci, and Lucas numbers, respectively, and thus the ratio of consecutive terms of Z converges to τ. Several new sequences of graphs (golden family graphs) were found ...

Let ψ denote the square root of the golden ratio, ψ = √

The Fibonacci sequence is one of the most beautiful and febulas mathematical concepts. Number turn in place that you have probably seen nature. a series numbers follows unique integers sequence. These generate patterns can be found all real life. are also called golden ratio. section used for architect, art, Space exploration, etc. Keywords: Numbers, Golden ratio

The Golden Section is proposed to be the preferred ratio in many domains. Starting with Fechner, there were several empirical studies concerning the preference of the Golden Section with inconclusive results. Our main concern is that the Golden Section can neither perceived no produced exactly since it is an irrational number. Therefore, we propose to give a closer look to preferences for ratio...

A close reading of Hotelling's famous article on exhaustible resources reveals the following passage: 'If a mine-owner produces too rapidly, he will depress the price, perhaps to zero. If he produces too slowly, his profits, though larger, may be postponed farther into the future than the rate of interest warrants. Where is hisgolden mean? And how does this most profitable rate of production va...