Just Another Fibonacci Number

0 Times
A "0 times" is, evidently, neither a convex nor a concave pile but no pile at all and the value contained therein will not be counted in the final result. It is represented by a dotted circle in the illustrations.

The value "0" does not have the same significance in the Fibonacci structure as it has in the exterior world of integers.
In the additive system, 0 is the central point (as it is in the Fibonacci system) and is neither positive nor negative (though it is often placed in the "positive camp"); it is an absence of all value with very definite characteristics: - no matter how often it is added or subtracted from a value, the original value remains the same.
In the multiplicative system, the value "0" does not belong at all since it represents the infinitely small, the limit of the mirror : no matter by whom it is multiplied, it is impossible to impart any value to the product, which remains invariably zero; it is not permissible to divide by it because the quotient would become infinitely large.

 2 1: 1. 1: 0 1: +1 0 0 +1 0 +1 -1 +1 -1 +1 +1 -1 +1 +2 -1 -1 +2 -1 -1 +2 -1 +2 -1 -1 +2 -1 +2 -3 +2 -3 +2 +2 -3 +2 -3 2 +2 -3 +2 +2 -3 +2 -3 +2 +2 -3 +2

However, in the Fibonacci system, the significance of 0 is quite different as
it is a number like any other, structured by the sum of the two preceding numbers
or by the difference of the two following numbers.
The series is structured in such a way that it goes right through the "central point"
without changing the way in which the values relate to each other.
Certain numbers (the 1s) have been prefixed or suffixed for precise identification :
. . . -3 +2 -1 +1 0 1: 1. 2 3 . . .

It is therefore possible to divide 0 into any number of parts producing, in each case, a very specific result. All these results will, of course, have a total value of the initial 0.

EXAMPLE : 0 divided into 89 parts is 34 parts of -55 plus 55 parts of 34
EXAMPLE : 0 divided into -55 parts is -144 parts of 89 plus 89 parts of 144