Balázs Halmos

Pentagons in medieval architecture

Among regular polygons, the pentagon is considered to be barely used in medieval architectural compositions, due to its odd spatial appearance and difficult method of construction. The pentagon, representing the number five has a rich semantic role in Christian symbolism. Even though the proper way of construction was already invented in the Antiquity, there is no evidence of medieval architects having been aware of this knowledge. Contemporary sources only show approximative construction methods. In the Middle Ages the form has been used in architectural elements such as window traceries, towers and apses. As opposed to the general opinion supposing that this polygon has rarely been used, numerous examples bear record that its application can be considered as rather common. Our paper attempts to give an overview of the different methods architects could have used for regular pentagon construction during the Middle Ages, and the ways of applying the form.

Golden Ratio and Fibonacci Sequence in Pentagonal Constructions of Medieval Architecture

Abstract The construction of the regular pentagon has always meant a difficult geometrical exercise for architects during the Middle Ages. As the correct drafting was forgotten after the Antiquity, several methods for its approximation had been invented in medieval times. As Golden Ratio appears between several parts of the regular pentagon, the role of the Fibonacci sequence in these approximate constructions is to be examined. The pentagonal drawing in the sketchbook of Villard de Honnecourt calls our attention to a possible way how medieval architects could have applied simple numerical ratios for getting angles they needed. The approximation of 72°, for instance, is likely to have been crucial for this pentagonal construction, as well as the approximation of Golden Ratio that could have been achieved by neighbouring pairs from Fibonacci’s sequence.

Problems of surveying profile shapes of gothic architectural fragments

The quest for the secret of geometric design methods and proportioning strategies of medieval master builders dates back to the middle of the 19th century. The improvement of surveying technologies allows adapting the advantages of laser-based instruments and computer aided analysis to the observation of this subject of revolving relevance. The subject of the paper research is to present the analysis of medieval architectural details from a geometrical point of view. In the current status of the research the paper focuses on the methodological aspects of the surveying process of gothic architectural fragments.

Analysis of Gothic Architectural Details by Spatial Object Reconstruction Techniques

The paper focuses on the 3D data acquisition technologiesthat support capturing the geometry of medieval architecturalfragmented stones. High-resolution models of such fragmentsenable the analysis of profile shapes as well as the markinglines and curves left by the instruments of stonemasons, andtherefore, indirectly, identifying connections between severalmaster builders could become possible. Considering therequirements of historical analysis and the fact that the investigatedstones are under monument protection, the authorsdecided to use remote sensing technologies, such as structuredlight scanning, terrestrial laser scanning, depth camera andimage-based reconstruction.The paper evaluates the discussed technologies based on theaccuracy and geometric resolution of the obtained 3D models.Besides technical parameters, time and cost requirements alsohave been investigated. The paper gives an overview on theadvantages and shortcomings of the applied data acquisitiontechnologies and of the provided end-products.