Talal Ghannam | Searcharxiv

arXiv2021

A Novel Geometric Model of Natural Spirals Based on Right Triangle Polygonal Modular Formations

We propose a novel class of spirals that are based on perfect polygonal formations. The spirals are defined by a fractal of right triangles that delineate their geometry and determine their progression rates and modes. We show how these spirals match naturally occurring ones, including hurricanes and galaxies, much better than already proposed models, allowing for more accurate categorization of these phenomena and better prediction of their physical properties.

math.GM↗

arXiv2019

Accurate and Infinite Prime Prediction from Novel Quasi-Prime Analytical Methodology

It is known that prime numbers occupy specific geometrical patterns or moduli when numbers from one to infinity are distributed around polygons having sides that are integer multiple of number 6. In this paper, we will show that not only prime numbers occupy these moduli, but non-prime numbers sharing these same moduli have unique prime-ness properties. When utilizing digital root methodologies, these non-prime numbers provide a novel method to accurately identify prime numbers and prime factors without trial division or probabilistic-based methods. We will also show that the icositetragon (24-sided regular polygon) is a unique polygon pertaining to prime numbers and their ultimate incidence and distribution.

math.GM↗