File:Математична (геометрична) модель атома.jpg

English: The mathematical (geometric) proof of the static theory of the structure of the atom consists in the assumption that the electrons of different layers are nothing but electromagnetic spheres that contact each other at the points indicated in the diagram. If we take the radius of the helium atom as a basis, then the area of the circle that passes through the center of the atom's nucleus will be 3.14 conventional units. Then the area of the sphere of the next electronic layer for neon - argon (a rhombus in the layer in the form of interaction between layers 2 and 3 of the period) with a sphere radius of 1.75 u.o. is 38.48 u.o. in a square Divide by 8 electrons. We obtain the area of the electron on the area of the electronic sphere of 2-3 periods of the table of elements, equal to 4.8 u.o. in a square We determine the radii of the spheres by the contact points of the layers of different periods. We calculate the areas of these spheres. For the boundary between the 4th and 5th period (radius 2.625 u.o.), the area of the sphere is 86.59 u.o. in a square For the boundary between the 6th and 7th periods (radius 3.5 AU), the area of the sphere is 153.931 AU. in a square We divide these areas of the spheres by the area of one electron (4.8 u.o. squared). We get discrete numbers: 18 and 32 areas of electrons are placed on the area of spheres. Conclusion: electrons of one period are packed in a single layer of 8, or 18, or 32 electrons, which corresponds to the number of elements in the periods of Mendeleev's table of elements