Pentagons in Medieval Sources and Architecture

Fehér, Krisztina; Szilágyi, Brigitta; Bölcskei, Attila; Halmos, Balázs

doi:10.1007/s00004-019-00450-7

Cited by 6 publications

(5 citation statements)

References 6 publications

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“…The idea originated from the 19th century when several speculative theories were developed concerning medieval design methods (Csemegi, 1953;Fehér and Halmos, 2015;2016). Medieval sources indicate that triangle, square and also pentagon formats (Fehér et al, 2019) were used for plan and detail design, but the logic for these approaches varies widely (Shortell, 2002;Wu, 2002). Without the original plans, any reconstruction of the design cannot exceed hypothesis.…”

Section: Theoretical Background 41 Medieval Design Methodsmentioning

confidence: 99%

Remarks on the Proportions and Dimensions Used in the Design of the Medieval Church of Zsámbék

Fehér

Halmos

2019

Period. Polytech. Arch.

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Since the 19th century, the church of Zsámbék was continuously a focus of scholars' interest. The present paper intends to research the church ruins with a new aspect. Using an accurate terrestrial laser scan survey, the geometry of the plan is analysed in order to find proportions among the dimensions. The main goal of the study is to gather information about the design logic of the first masters of the 13th-century Premonstratensian abbey. In addition, our goal was to detect contributions to the 13th-century construction history of the church, that cannot be found in archives of graphic sources. The latest archaeological excavation achieved excellent results concerning several crucial historical points; however, the periodization of the church is still not entirely clarified. From the 19th century, different scholars have proposed various hypotheses about this topic, without consensus.

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Section: Theoretical Background 41 Medieval Design Methodsmentioning

confidence: 99%

Remarks on the Proportions and Dimensions Used in the Design of the Medieval Church of Zsámbék

Fehér

Halmos

2019

Period. Polytech. Arch.

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“…Fehér et al [2] note in an interesting research work on the regular pentagon: "The occurrence of pentagons in medieval architecture tends to be considered as rare; scholars have suggested that its correct geometrical construction was unknown among artists or architects until the early 16th century", but their paper "provides a series of architectural examples containing pentagonal forms highlighting that its role in the design process of medieval masters was much richer than it is currently considered" [2]. "Half decagonal apses, pentagonal traceries, and even design details were related to geometric methods based on the construction of a regular pentagon", which was also used "in plan design of monumental constructions such as the cathedrals of Reims and Saint Quentin" [2].…”

Section: Divine Proportionmentioning

confidence: 99%

Cassinian Directorial Surfaces Modelling as Geometric Pattern in Designing Architectural Structures

2023

Teh. vjesn.

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In this paper we propose a method for the genesis of novel geometric surfaces which we named Cassinian directorial surfaces (CDS). They represent spatial geometric locus of points whose product of distances from k fixed directrix lines is constant and given by the parameter S. The modelling of such Cassinian directorial surfaces is based upon two criteria that are the geometric mean as a proportional harmony and the golden ration i.e. the divine proportion. The three particular spatial dispositions of directors-directrices thus enable the design of three types of Cassinian five-directorial surfaces: CDS1 incorporating directrices which coincide with the sides of a regular pentagon; CDS2 incorporating directrices coinciding with the edges of an upright regular pentagonal prism; and CDS3 incorporating directrices which coincide with the skew diagonals of the sides of an upright regular pentagonal prism. In addition, for each type of the surface we propose possible applications of such surfaces as a geometric pattern in designing architectural structures.

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“…(Raynaud, 2012) Patrimonio della cultura islamica è un ingegnoso metodo approssimato per disegnare il pentagono. (Fehér, 2019) Il metodo si basa sulla proprietà che la lunghezza dell'arco BC del cerchio ABC è uguale a 2×OA×sin(α/2), dove α è l'angolo centrale ( Fig. 3).…”

Section: Pentagoni Regolari E Approssimatiunclassified

Il pentagono come strumento per il disegno delle fortezze

Magnaghi-Delfino

Mele

Norando

2020

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The pentagon as a tool for fortresses’ drawingStarting from the fifteenth century, the diagram of many fortresses has a pentagonal shape. Among the best known fortresses, in Italy we find the Fortezza da Basso of Florence, the Cittadella of Parma, the Cittadella of Turin, Castel Sant’Angelo in Rome. The aim of this article is to analyze the reasons that link form and geometry to the planning of the design and the layout of pentagonal fortresses. The pentagon is a polygon tied to the golden section and to the Fibonacci sequence and it is possible to construct it starting from the golden triangle and its gnomon. This construction of the pentagon is already found in the book De Divina Proportione by Luca Pacioli and is particularly convenient for planning pentagonal fortresses. If one wants to draw the first approximated golden triangle, one can just consider the numbers of the Fibonacci sequence, for example 5 and 8, which establish the relationship between the sides: 5 units is the length of the base and 8 units the length of the equal sides. In the second isosceles triangle, which is the gnomon of the first, the base is 8 units long and equal sides are 5 units long; half of this isosceles triangle is the Pythagorean triangle (3, 4, 5). This characteristic of the golden triangles, that was already known by the Pythagoreans and, in a certain sense, contained in the symbol of their School, allows to build a pentagon with only the use of the ruler and the set square. The distinctive trait of the construction just described makes preferable to use the pentagon in the layout of the military architectures in the fieldworks. We have verified the relationship between numbers, shape and size in the layout of Castel Sant’Angelo (1555-1559) in which the approximate pentagon was the instrument for the generation of its form.

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Pentagons in Medieval Sources and Architecture

Cited by 6 publications

References 6 publications

Remarks on the Proportions and Dimensions Used in the Design of the Medieval Church of Zsámbék

Remarks on the Proportions and Dimensions Used in the Design of the Medieval Church of Zsámbék

Cassinian Directorial Surfaces Modelling as Geometric Pattern in Designing Architectural Structures

Il pentagono come strumento per il disegno delle fortezze

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