Copyright © Klaus Piontzik  
German Version 
There is the possibility of getting an even better adjustment for the numbering values. Based on the linearization, an exact numbering can be calculated. The following applies: 
Rearranging the equation according to x gives 
7.6.1  Equation: 
The following applies:
b = ln w_{0} a = Δ y/Δ x Δ y = ln w_{n} – ln w_{0} Δ x = n_{new} Inserting all terms gives: 
7.6.2  Equation: 
With the new numbers you get a logarithmbased number sequence
that corresponds to the initial values. This new numbering then
reflects the harmonic structure of the arrangement under investigation
and can be viewed as a new scaling.
If you replace ln by log and e by 10 in all equations, the entire consideration and function determination also applies to base 10. 
200 sides, 23 of them in color 154 pictures 38 tables Production und Publishing: ISBN 9783735738547 Price: 25 Euro 
