The metrics include four constants: Ludolph number (p=3.1415…), Napier number (e=2.7182…), golden ratio (F=1.6180…) and so-called “irrational one number” (j=1.0079…). The term “irrational one number” was suggested by the author for the first time. Moreover, the constant j=1.0079… simultaneously coincides to the value of atomic mass of hydrogen with high accuracy. It is the most wonderful property of this mathematical expression. Also we can see that mathematical metrics of atom of hydrogen describes the substance, the mass, the length and the form simultaneously. Thus the expression may be used as universal system of measurements (metrics) for analysis of atoms.

There is accurate view of mathematical metrics of hydrogen atom:

certainly it mean that 

where

j=1.0079…

Ф=1.6180…

e= 2.7182…

=3.1415…

and 

It is good visible that four mathematical constants , e, Ф, j are closely connected to the idea of hydrogen atom. The view of this hydrogen metrics looks like theoretical hint concerning complicated internal logical structure of the atom. Also there is probably reflection of logical properties of hydrogen atom. The perspective of logical programming of atoms and elementary particles seems visible in future. That is why the metrics as model task may be useful for testing together with logic and accuracy of quantum computer.