Geometric constructions embody mathematical relationships, theat nowadays are known as part of trigonometry. It is this mathematical attribute of geometric models that facilitates the research in the plant design. Transforming geometric constructs into form dimensions provides a comparison check with the actual measurements at the castle.
Naming the plant form dimensions as mathematical variables and organizing the mathematical relationships for these variables into a sequential collection makes up a seeming mathematical algorithm. The developmnts in the geometric operations, such as in the Concept Plant Design, are matched by a series of mathematical definitions in the mathematical model.
The parallel modeling con equivalent algorithms, geometric and mathematical, provides a natural and methodic approach to theorize and test geometric constructs for the plant design of Castel del Monte during the study, by comparing results to the actual plant forms and dimensions.
Going beyond decoding and verification the plant design, the mathematical model allows to study and identify with certainty the unit of measurement used at Castel del Monte.
Besides being an essential tool to study the plant design, the mathematical model reveals a high level of mathematical sophistication at the height of the Middle Ages. It shows a rigorous and scientific approach in the structural design of an edifice, albeit within the limited scientific knowledge of the times.
The complex design algorithms and the peculiar geometric manipulations are too sophisticated to have happened in one genial inspirational moment or as the fruit of masonry construction tryouts. They were the result of iterative design processes, working with geometric models, supported by mathematical formulations, and possibly including some physical models as well, Fig. 1.
Figure 1. Physical modeling of minor diagonals.
Scholars that have instinctively described Castel del Monte as a model of mathematical precision do not know how true that characterization is, because there is a mathematical model at the basis of the plant design.