## 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 3 ^{rd} 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 3^{rd} 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:

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 2^{nd} 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 1^{st} to the 2^{nd} 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 R*b*/R*c*=.

The total mathematical correction from the point-volume (1^{st} dimension) to our 3^{rd} 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**