The Transformation to the third Quantum Dimension (Bohr-distance)
When you are interested in physics you must read “Unbelievable“!
We demonstrated that with 
/2 point-volumes we can create a perfect “circle” with 864 triangles OAB. Point O (figure 4) is the center of the created Compton quantum circle (Rc). Between O and Rc the quantum space is imperfect. The “bulbs” with radius QD cannot fill up spherical space homogeneously.
The “perfect” geometry is created at Rc. For the observer in O it is not possible to observe perfect circles all around (no perfect bulb possible when space is filled with point-volumes).
The orientation of the two possible circles Rc is not fixed.
With the “perfect” two-dimensional circle Rc we are able to create a perfect bulb shell tunnel with diameter Rc at the distance *Rc; the Bohr-distance.
Figure 6. Compton circles creating the 3rd quantum dimension.
With /2 circles Rc (two circles each) we are able, in conjunction with the creation of the Compton-circle, to create two “perfect” bulb shell tunnels with radius Rc at the Bohr-distance; the beginning of the 3rd quantum dimension.
The ratio between the distances Rb and Rc should be .
We have observed that the ratio between the Bohr-radius and the Compton-radius is:
(14)
The Bohr/Compton distance ratio appears to be 10.8674 times larger than the ratio Rc/QD or the Rydberg/Bohr ratio.
We must however not forget that the situation at 2-QD is not the same as the 1-QD level or the 3-QD level. We have seen that a mathematical correction from 1-QD to 2-QD with the factor 2pi was necessary. We now compare the 3rd dimension of the Bohr-bulb with 2nd dimension of the Compton-plate. A mathematical correction is necessary.
The factor 10.8674 is the correction factor from the 2-QD to the 3-QD. From the 1st to the 2nd QD the correction factor is 2π. This transformation explains the origin of the mathematical natural constant π. Is it a coincidence that the other mathematical natural constant e can be found in 10.8674, because 
and the difference is therefore only 0.05%? **
So both mathematical natural constants may well originate from the dimension transfer from the point-volume to three-dimensional space.
After the dimension correction we have also the ratio Rb/Rc=.
The total mathematical correction from the point-volume (1st dimension) to our 3rd dimension is: 
.
(** When we correct for neglecting the factor (1+Me/Mp)=1.0005446, when equation 5a was derived from 5, the deviation factor with 4*e is less than 2.10^-5)
Next chapter: The 12 Ionization Levels of the Atom
