The role of the 'silver ratio' in the geometry of Castel del Monte

The aim of this work is the study the Castel del Monte plan by means of geometrical relationships based on the golden ratio and silver ratio. Particularly, we emphasized the aspects of the silver ratio. There are some observations regarding that certain octagonal plans of historical buildings hypothetically influenced Frederick II in the choice of octagonal geometry for the plan of the castle. From this point of view, we moved to the discussion of the golden ratio and the silver ratio, and to the application of the two metallic ratios in the analysis of the Frederician castle geometry. Moreover, the construction of the castle's ideal plan is proposed in which only the silver ratio has been used. In this case, the geometric proportions between the parts remain harmonious and some slight differences in the castle plan, which is based on the golden ratio and silver ratio, are removed