Silver ratios, Cardano’s formula, and visual model of the second atomic shell

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Author: 
Alexander V. Yurkin
Abstract: 

This work is devoted to geometrical research of the ray trajectories system. We consider trajectories of electrons moving in the second shell of an atom. The proposed model of movement of electrons is based on the geometrical interpretation of the Pauli Exclusion Principle and the geometric interpretation of distribution of electrons in energy levels, shells, and subshells of atoms in Mendeleev’s periodic table. It turned out that the second shell can be described by a cubic equation, Cardano’s formula, and a new system of triangles as well. We present some new geometric ratios - silver ratios - between the elements of our model and the triangle system (the ratios between the sides, angles and areas of triangles). In the paper, we show that it is possible to describe atomic shells geometrically using complex numbers, and generalize our approach to geometric interpretation of the rest atomic shells. In the Appendix we apply the silver ratios to show the images of a silver parallelepiped and examples of silver houses and we compare our trajectories system with trajectories of car driving.

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