At R = o both non-Euclidean spheres transform into the Euclidean plane and according to the equation (4) holds:
2 Calculation of the theoretical inverse fine structure constant in the Euclidean plane
The theoretical inverse fine structure constant in the Euclidean plane is calculated with the help of the equation (29).
If the sphere curvature on the atomic level equals the curvature of the hypothetical elliptic observable universe, the inverse fine structure constant should not significantly differ from the theoretical constant in the Euclidean plane.
In the Euclidean plane there exists one restriction: c < a.
In the Euclidean plane geometry parabola is the locus of points equidistant from a fixed line (directrix) and a fixed point (a focus) not on the line.
2] or the spheroid is most often used and locally their surface is approximated by the Euclidean plane tangent in a given position.