Re: Sum of periodic functions with incommensurate periods

This subject is trivial on certain levels. One is
the sum of one algorithm that deals with irrational numbers A. Greeks like Archimedes solved this issue without our modern limit theorem, by finding the area/volume of a parabola by a 1/4th geometric
series, stated as:

4A/3 = A + A/4 + A/16 + ... + A/4n+ ...

with A being any number, even pi or any irrational.

But Archimedes solved it in an exact form, or

4A/3 = A + A/4 = A/12

using the older Egyptian fraction notation.

All this means that our 400 year old base 10 decimal system generally can not sum periodic functions with incommersurate periods. A change in the numeration system to a finite form is required in many cases.

Good hunting,

Milo
.