Ossendrijver identifies the Saturn System B sigma and tau zig zag functions to be of the form of template ZZ.A.1. This template having the defining parameters:
m is the minimum, smallest one, or depth;
M is the maximum, largest one or height; and
d is the difference (addition or subtraction).
The template ZZ.A.1 does not explain when to add d or subtract d but other templates do provide an explanation. The other templates define a reflection point at the maxima M such that if the current value of the function being calculated has exceeded
M the reflection point is reached and the next step is to commence a subtraction of
d has. A similar reflection point occurs at the minima
m.
The following chart shows a zig zag function with parameters m = 11, M = 14 and d = 1/5 similar to the Saturn System B. I have deliberately changed the y axis to start at 10 rather than 0 to emphasise the shape of the function:
This chart closely matches the shape of the corbel ceilings of the chambers of the Red Pyramid. In particular, the upper chamber of the Red Pyramid. The Upper Chamber has been assessed in a new paper released by Monnier available here: [
www.egyptian-architecture.com] and is found to have 13 corbels. The chart above was for an simplified System B zig zag function. If we use the Babylonian sigma zig zag function:
Quote
Ossendrijver
For Saturn: the height is 14;4,42,30, the depth 11;14,2,30, the difference 0;12; thus the positions.
here m = 11 + 4/60 + 42/60^2 + 30/60^3, M = 11 + 14/60 + 2/60^2 + 30/60^3 and d = 12/60 or 1/5. Using the full Babylonian System B expression, we would expect to find approximately 13.5 steps of difference
d before we hit the "reflection" point. Monnier tells us there are 13 corbels but in his diagram the sixth corbel is much taller than the other corbels - from measurement of Monnier's diagram about 25-30% higher meaning we have the equivalent of about 13.25 corbels in height. Could the corbel ceilings here be a representation of the Saturn System B sigma zig zag function?
References:
Ossendrijver, M., Babylonian Mathematical Astronomy: Procedure Texts, Springer, pp 43-44, 309-310