Footing Width f
The footing width, labeled f in the presentation, has a much greater role and impact in the geometric design than this feature seems to convey as an architectural ornament.
It defines the footing width of course; it is an integral component in the façade and tower wall definition; it is a component in the determination of the room width; it defines the lateral offset of the base octagon minor diagonals in determining the cross vault centerline intersections; and it defines the recession of the indoor face of the walls on the upper floor on the façade and courtyard sides.
As it turns out and will be shown in the measurement section, the measure of the footing dimension is an irrational number. It is an odd measure, difficult to define physically without an accurate ruler, whose existence is difficult to imagine in the Middle Ages.
The footing width is one variable in the concept design that is not derived geometrically but was assigned a measure, one eight the measure of the tower octagon side. This is a practical way of defining the footing measure in the field – dividing equally the side of the wall, three times over.
The lack of geometric dependency for f in a design where all other variables have a geometric genesis is logical because the footing feature is an arbitrary geometric appendage. By relating the footing measure to the tower octagon side, the architect made the footing-width a dependent variable in the geometric design.
It can be anything that the architect chooses it to be; but it does affect all other forms defined after its introduction in the geometric design sequence, right after the definition of the tower size and dimension.
The number eight is the mystical number of Castel del Monte. In the mysticism of the Middle Ages, numbers had symbolic value besides serving as measure. It is therefore not surprising that the architect chose eight as the ratio between the side of the tower octagon and the footing.
It is likely that the concept for a footing for the tower may have been related, in the mind of the medieval architect, to the resolution of the structural forces and the associated masonry requirements, although we cannot figure how.
A tower footing is also a feature at other castles built by Frederick II. More could be learned on this subject by studying the footing of these other structures.