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...

In this paper we propose an efficient and secure (SPA resistant) elliptic curve scalar multiplication algorithm over odd prime fields. For this purpose, we propose an explicit algorithm for short addition-subtraction chain method which utilizes a golden ratio. We term it as golden ratio addition chain method or GRAC method in short. Our proposed scalar multiplication algorithm based over GRAC m...

The Cluster Editing problem asks to transform a graph by at most k edge modifications into a disjoint union of cliques. The problem is NP-complete, but several parameterized algorithms are known. We present a novel search tree algorithm for the problem, which improves running time from O(1.76 + m + n) to O(1.62 + m + n) for m edges and n vertices. In detail, we can show that we can always branc...

Through about 130 years of the history of experimental aesthetics, preferences of figures have been summarized in representative values such as the golden ratio. Researches especially in the golden-section hypothesis overshadowed the basic and profound problem of how people's individual preference would be decided. In the present study I returned to simple quadrangles, and investigated each per...

So what is beauty? First let me perhaps surprise you by stating that beauty can be defined numerically:1.6180339887. That is beauty that is the golden ratio (fig 1). It was described by the Pythagorean mathematicians, as they kept seeing this ratio in things regarded as beautiful, and it was first written down by Euclid, and can be expressed either as a linear relationship or as a shape, in eit...