Concept Design Enlargement Consideration
Given the premise that there may have been a need to enlarge the open space inside the tower, the questions next are by how much and by which geometric means to accomplish the enlargement.
The first thought is a straightforward geometric enlargement, but this was not the choice.
In the concept design, all forms expand in geometric proportions like figures on an inflated rubber ball. Changing the dimension of one form causes the dimensions of other forms to change accordingly, in geometric proportions.
All form dimensions are dependent functions of a single variable, which is the measure of the base octagon, measured by its diagonal.
Therefore, a straightforward enlargement of the open space inside the tower involves an enlargement of the tower and likewise an extension of the base octagon.
The major diagonal D of the base octagon is nearly 18-times the tower center opening measure y in the concept design. An enlargement of the open space inside the tower would require a corresponding enlargement, 18-times bigger, of the base octagon diagonal, because of the geometric interdependency. For example, enlarging the open space inside the tower by one meter entails increasing the major diagonal of the base octagon by nearly 18 meters.
While no dimensions have been discussed in this purely geometric procedure, the diagonal of the base octagon is about 56 meters. Enlarging the open space inside the tower and maintaining the geometric proportionality is not a viable course; the result is an enormous enlargement of the castle. The limited space on top of the hill puts constraints on the castle dimensions, which would be a deterrent to enlargement, folio 103:01.
There is also another consideration that rconstrains changes in the plant dimension. The orientation of a new important edifice was connected to religion and astrology in antiquity. Similarly, its dimension was typically determined by religion, mysticism, and astrology. This was the case for Castel del Monte as well, with the portal facing east and the size tied to religious and astrological notions. This is the religious and mystical formulation for the size of this castle, a matter addressed separately (Design Math Model).