Volume: 1.3 Open Access Journal Adv Comput Sci Volume: 1.3 1 Advances in Computer Sciences ISSN 2517-5718 New Analogues of the Pascal Triangle and Electronic Clouds in Atom Alexander Independed researcher, Puschino, Moscow, Russia Article Information DOI: 10.31021/acs.20181114 Article Type: Research Article Journal Type: Open Access Volume: 1 Issue: 3 Manuscript ID: ACS-1-114 Publisher: Boffn Access Limited Received Date: 10 November 2018 Accepted Date: 20 November 2018 Published Date: 22 November 2018 *Corresponding author: Alexander Yurkin Independant Researcher 142290, D-20, app. 56, Puschino Moscow, Russia E-mail: alvl1yurkin@rambler.ru Tel: 9853887590 Copyright: © 2018 Yurkin A. This is an open- access article distributed under the terms of the Creative Commons Attribution 4.0 international License, which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited. Citation: Yurkin A. New Analogues of the Pascal Triangle and Electronic Clouds in Atom. Adv Comput Sci. 2018; 1(3):114 Abstract A new flat analogue of Pascal’s triangle based on the consideration of parts of regular polygons (regular hexagon, regular icosagon, etc.) is proposed. The classification of nuclear models of an atom is clearly shown: with circular, elliptical, cloudy and belt orbits of electrons. The belt model of atom consisting of a system of rays, a layer of electrons moving along wavy trajectories can be represented as a “cloud of trajectories.” A comparison is made of various types of wavy trajectories: a broken wavy trajectory, the trajectory made up of parts of a regular polygon and the sinusoidal path. It is shown that many calculations for our system of rays can be performed not only for rays that are inclined at small angles (small- angle paraxial approximation), but also for rays that are inclined at any angles, the results of such calculations will coincide. It has been suggested that it is possible to more fully explain the origin of the splitting of atomic spectral lines and fullerene schemes construction. Keywords Pascal triangle; Electron; Trajectories; Regular Polygon; Fullerene; Geometrization of physics Introduction 1. Statistics and computer science have grown as separate disciplines with little interaction for the past several decades. This however, has changed radically in recent years with the availability of massive and complex datasets in medicine, social media, and physical sciences. The statistical techniques developed for regular datasets simply cannot be scaled to meet the challenges of big data, notably the computational and statistical curses of dimensionality. The dire need to meet the challenges of big data has led to the develop Geometric models of the atom consist of lines and geometric shapes (Figure 1). The nuclear models of the Bohr atom [1,2] and Somerfield [1,2] are based on the Kepler planetary model [2] with circular (Figure 1a) or elliptical (Figure 1b), respectively, electron orbits rotating around the atomic nucleus. There are nuclear models of atoms consisting of a nucleus and electron clouds [1] of various configurations, for example, in the form of a torus (Figure 1c). The geometric figures of the models shown in Figure 1 contain different, relatively large and relatively small distances: Δ>>δ (1) and R B ~ Δ, (2) Where Δ is the thickness of the layers of the electron orbits or the electron cloud, δ≈2*10 - 15 [m] is the thickness of the individual electron orbit (approximately equal to the size of the electron [3]), and R B ≈5,3*10 -11 [m] is Bohr radius. The value of δ in comparison with the values of Δ andR B is small. 2. In [4], based on a consideration of the system of rays, a new geometric belt nuclear model of the atom was proposed (Figure 2). In this work, it was shown that this model Figure 1: Geometric models of the atom consist of lines and geometric shapes Yurkin*