The book is devoted to research of distribution of light in narrow beams of light (including laser beams). Such approach corresponds to approach of the great Italian physicist and mathematician and Jesuit F.M. Grimaldi. As early as 17th century he was engaged in researches of narrow beams of light for clarification of the nature of light and discovered the phenomenon of light diffraction. Our calculations are based on consideration of binomial distributions. The correlation of distribution of rays and the system of numbers placed in the three-dimensional table, the nonlinear arithmetic pyramid is shown. Two types of nonlinear arithmetic triangles are considered. Communication with binary notation is shown. Results of numerical calculations of binomial distribution of the second (nonlinear) type for big power of binomial are given. The ray analog of wave model of light and Huygens-Fresnel's elementary waves on the basis of consideration of geometrical model is offered. Examples of possible application of our geometrical model in various areas are given. The book is intended for all who interested in novelties in mathematics, optics and other areas where geometrical models are used.