# Fine-structure constant

Corresponding Wikipedia article: Fine-structure constant

The fine-structure constant is a dimensionless quantity, which connects some fundamental constants to each other $\alpha=\frac{e^2}{2\varepsilon_0 hc}\tag{1}$

Obviously, the dimensionless constant has a geometric meaning. The perfect knowledge of the particle's aetheric vortex geometry would express the Planck constant using other fundamental constants without the fine-structure constant.

A geometric expression of the fine-structure constant by Basil Shabetnik [1] is used in the following reasoning.

The numeric value can be expressed as $\frac{2}{\sqrt{\alpha}}=23,4\tag{2}$

Let (2) is the closed path length of an aetheric beam with a nominal wavelength of $$2\pi$$. The first approximation for a proton (see "Magnetism of particles") is $\frac{2}{\sqrt{\alpha}}\approx 6\pi\tag{3}$

The proton monad distorts and lengthens the beams. The curvature shape is a stellated octahedron-based fractal. The lengthening factor is the fractal dimension of Koch curve, which is the edge of stellated tetrahedron. The second approximation is $\frac{2}{\sqrt{\alpha}}\approx 6\pi\frac{\ln 4}{\ln 3}=23,8\tag{4}$

On the other hand, the beam paths are not circular, but they are the inscribed polygonal chains, which approximate the circular paths. The beam path contraction is taken into account in the exact formula with a correction of $$\pi$$ $\frac{2}{\sqrt{\alpha}}\approx 6(\pi-\Delta)\frac{\ln 4}{\ln 3}\tag{5}$ $\Delta\approx 0,05$

This correction is close to the correction for a planar polygon with 10 vertices that is consistent with the 8 vertices of a stellated tetrahedron.

## References

1. Basil D. Shabetnik, Fractal Physics. Science of the Universe. (Ch. 4.1)