Before going to the mathematics of this number system, I thought that it would be good to show the exact results of the calculation of the g-factors of proton and neutron (g-factor is ‘dimensionless quantity characterizing the magnetic moment and angular momentum of a particle’).
Explanation.
There are three constants taken into account: P, F, and S. I am looking for all the sets of singles (three), pairs (six), and triplets (six). The order is very important. Altogether, there are fifteen different sets. The set above is in P-F-S order, with pairs (e.g., F-P, P-ST, and then ST-FT, FT-PT, and so on, going upwards from the bottom - S-F pair gives P). Those pairs are the multiplication of the two adjacent constants in one way, and the division in another way. Inverses of constants are included. From this table are taken the values of transcendental constants used in calculating exact results agreeing with experimental results of measurements of the proton g-factor, neutron g-factor, muon and electron g-factor plus g-2 factors (i.e., magnetic moments) of the electron and muon.
There will be posted three more Tables, one the multiplication/division table of constants going down; and two addition/subtraction tables of constants going up and going down. They are necessary to calculate the measured values of the g-factors mentioned above. I did not have the time to write FORTRAN codes to obtain those tables. I am going to do it in the future with double and quad precision. If you notice any errors, please understand that all these values are calculated by hand on an HP Prime calculator with 12-digit precision.
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