Ray system in lasers, nonlinear arithmetic pyramid and nonlinear arithmetic triangles

TL;DR

This paper explores the geometric and combinatorial properties of laser ray systems, nonlinear arithmetic pyramids, and triangles, revealing correlations with binomial coefficients and integer partitions.

Contribution

It introduces a novel analysis of laser ray systems and their relation to nonlinear arithmetic structures, expanding understanding of their mathematical properties.

Findings

Correlation between laser rays and binomial coefficients

Description of nonlinear arithmetic pyramids and triangles

Analysis of integer partitions in nonlinear arithmetic contexts

Abstract

The paper describes a system of rays declining at small angles in lasers. The correlation between a group of rays and binomial coefficients is shown. The correlation of distribution of rays in the system of numbers placed in a three-dimensional table, the nonlinear arithmetic pyramid is shown. Two types of nonlinear arithmetic triangles are considered. Various types of partitions of integers is described.