Symmetric triangle of Pascal and arithmetic parallelepiped

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The book is devoted to the geometrical description of narrow beams of light and other processes in long tubes. In this work the symmetric (symmetrically numbered) Pascal's triangle is described and the new evident model a nonlinear arithmetic parallelepiped, for the numerical description of binary rays system and for an illustration of process of distribution of the branching system of paraxial (Gaussian) beams and wavy trajectories is offered. The offered new model can be useful to approximate and formal, but evident geometrical interpretation of processes of the movement of particles and waves in long pipes. It is possible to refer to such processes, for example, distribution of light in lasers, finding of a particle in infinitely deep potential hole (including new geometrical interpretation of a particle spin), laminar and turbulent flow of liquid in pipes, etc. A large number of drawings and schedules, and also tables with the numerical calculations executed in the Excel program are given in the book. The book is intended to all who is interested in new evident geometrical researches in the field of physics and optics.

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