The Geometric Design of Castel del Monte
This site outlines a study in the design of Castel del Monte, specifically how the medieval architects came up with this design.
The perfect forms and layout of the masonry at Castel del Monte is evidence that geometry is the theme and the guiding hand in the design of this castle.
Scholars and writers have invariably come to this conclusion, often speculating on what may have been the design process.
This study identifies the geometric design for the plant layout of Castel del Monte,
providing a unique window in the design knowledge and means at the height of the Middle Ages.
The presentation is divided in various sections, as indicated in the home page and outlined below.
Section I and II
The design starts with the ground plan. This is the key portion of the overall design, because it addresses the fundamental question of cross-vault construction and their support for a stable edifice.
The plant design process is divided in two parts.
1. The concept design for the plant layout (Section I)
This is the creative process where a series of geometric constructions follow starting from a square and ending up with an octagonal plant with octagonal towers at each corner and an octagonal courtyard. This gives the design the forms and look that is seen nowadays in the plant layout.
2. A systemic modification to the concept plant design (Section II)
This is a modification to the concept design in small details that are imperceptible to the eye, preserving the overall look of the plant design. The modification is a small enlargement of the octagonal tower, followed by a similar small relocation of the tower and a readjustment to the walls, in a similar change that affects all towers.
This is different from other changes that followed later in the design directed at specific portions of the castle, such as the modification at the entrance wing of the castle to accommodate a portal with portcullis.
The motivation and contemporaneity of this systemic change at the towers is a matter to wonder about—a theorized explanation in this study is that the architects felt a need to increase the open space inside the tower, without changing much the overall design first set in the concept phase.
However, the modification is an essential part of the design that brings the measures in the design model to match exactly the measurements at the castle. It also explains many details such as the seemingly irregular form of the tower octagon, the roof spandrels discovered by H. Götze, and others.
The research is essentially a study of geometric forms and manipulations, and involve extensive graphics. The presentation is an outline of these graphics with related explanations. The graphics are presented in sequence, following the evolution of the design.
The original drawings were prepared on slide presentation software. Their accuracy is limited by the graphical limitations of the software, but serve superbly for the intended illustration purposes.
The graphics are rendered on these pages either as PDF-file inserts or as JPG-files. The PDF inserts provide sharper graphics than the JPGs.
The study presentations are detailed and use PDF-based graphics. They are viewed best on large screen devices with full PDF-enabled browsers.
The resentations, including graphics, become demanding reading at times, especially in the second phase of the design. They provide detailed analyses, essential evidence that explains and supports the findings.
Slide presentations are included as shortcut alternatives, givinge more compact overviews of the design algorithms.
Section III addresses measurements and naturally deals with the unit of linear measurement in the design and construction of Castel del Monte.
The design outlined in sections I and II is a geometric algorithm that ties the final and complex design of the plant to a primal geometric form, the square. The tie is a series of geometric derivations that creates a chain of dependencies.
A key feature of this algorithm is that not only the geometric forms, but the dimensions as well are tied and dependent between the primal square and the final design layout. The dimensions of all forms in the final plant layout are related to the dimension first set for the primal square.
Only one quantity is needed in this design algorithm, a single measure that defines the size of the base square. All plant measures are then derived from this dimension: the size of the plant octagon, the size of the towers, the width of the walls, the size of the rooms, etc. This provides a means to explore and find out what is the linear unit of measurement that the medieval architects were working with.
This is done by creating a mathematical model of the design algorithm. The mathematical model is an orderly collection of mathematical formulas that define the measure of new geometric forms as the design process advances.
H. Götze theorized that the unit of linear measurement at Castel del Monte is the Roman foot. The mathematical model is useful to test for different measures of this "foot", comparing the results to the actual measurements at the castle.
The search is actually a bit more complex, because there are two unknowns: the dimension of the primal square, and the length of the "foot". There are, however, insightful clues from the religious mysticism of the Middle Ages as well as the actual measurements of the castle that help in this search.
Section III shows the results of this research, and identifies the linear dimension of the “foot” that was used by the medieval architects at Castel del Monte.
Section IV provides a historical look at the construction technology of cross vaults and relates the work at Castel del Monte as it contrasts with the tall cathedrals that were prevalent in central-northern Europe during the same medieval period.
The lack of detailed elevation data in the literature makes the study of the elevation design more challenging. Research in the design of elevated structures is an ongoing work, based on available data.