ANALYSIS OF THE APPLICABILITY CRITERION FOR K MEANS CLUSTERING ALGORITHM RUN TEN NUMBER OF TIMES ON THE FIRST 25 NUMBERS OF THE FIBONACCI SERIES

In this research investigation Analysis Of The Applicability Criterion For K Means Clustering Algorithm Run Ten Number Of Times On The First 25 Numbers Of The Fibonacci Series is performed. For this analysis RCB Model Of Applicability Criterion For K Means Clustering Algorithm is used. K-means is one of the simplest unsupervised learning algorithms that solve the well-known clustering problem. K- Means clustering algorithm is a scheme for clustering continuous and numeric data. As K-Means algorithm consists of scheme of random initialization of centroids, every time it is run, it gives different or slightly different results because it may reach some local optima. Quantification of such aforementioned variation is of some importance as this sheds light on the nature of the Discrete K-Means Objective function with regards its maxima and minima. The K-Means Clustering algorithm aims at minimizing the aforementioned Objective function. The RCB Model Of Applicability Criterion for K-Means Clustering aims at telling us if we can use the K-Means Clustering Algorithm on a given set of data within acceptable variation limits of the results of the K-Means Clustering Algorithm when it is run several times. KEY WORDS: K-means clustering algorithm, RCB model and Cluster evaluation.

Fibonacci series from power series

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

Is there a Similiarity between Fibonacci Sequence and Euler’s Number with Respect to Quantum Perspective Model?

According to Quantum Perspective Model, this article studies whether there is a link between the Euler’s numbers and the Fibonacci series. When the digits of the Euler’s number after the comma are converted from decimal(10) number base system to binary(2) number base system, it corresponds to the number in the Fibonacci series.(0,1,1,2,3,5,8,13,21,34,55...)[7].From this point of view, when the first hundred digits of the Euler’s numbers after the comma were calculated, the number "55" (ten times) in the Fibonacci series was found, in particular. Besides, the eleventh number in the Fibonacci series is also "55".In other words, the approximate unchanged numbers of the golden ratio numbers after the comma can be reached for the first time after dividing them from “55” to “34” (1,618). In sum, Euler’s numbers are not only attributed to the Fibonacci series in mathematics, but also attributed to the golden ratio in nature.

Some Properties on Divine Kaehlerian Manifold

Fibonacci sequence and the divine ratio are intimately inter-connected. In the Fibonacci sequence each number is the sum of previous two consecutive numbers and the ratio of any two consecutive numbers reflects the approximate value of divine ratio. The relationship between divine ratio and Fibonacci series is well express in divergent faunal anatomy and floral as well as their morphology. The present article is intended to study the properties of divine Kaehlerian manifold in terms of Fibonacci sequence, trace & eigen values of divine structure including its almost complex structures. Some properties of induced structures, theorems and propositions related to it have also been studied.

THE BEGINNINGS OF THE SELF-DEVELOPMENT OF NATURE AND THE PERIODIC SYSTEM OF CHEMICAL ELEMENTS OF D.I. MENDELEEV

Metaphysical methods of self-organization of harmony predict the beginning of the formation of the structure of a natural chain of chemical elements of matter. The trajectories of the sequence of chemical elements follow the Mendeleev-Luc, Fibonacci series and the paired principle periodicity (recurrence) of Nature. A digital model of the trinity of elements of the Periodic system connects neutrons, electrons and mass numbers of nuclei of elements and forms constants of their relations. It is confirmed by the formula of the proton-neutron theory of the atomickernels D.D. Ivanenko and V. Heisenberg. A comparison of experimental data with a theoretical prediction of the evolution of chemical elements showed them consent. The subsequent stages of the self-development of plants and animals follow the principles of self-organization of chemical elements, material whose memory displays their formation. The unity of the stages of self-development of systems on Earth is interconnected with the diversity of Nature. It confirms the interdisciplinary hypothesis of metaphysics that people think by the laws of Nature.