Il pentagono come strumento per il disegno delle fortezze
[EN] 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...
| Autores: | , , |
|---|---|
| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | italiano |
| OAI Identifier: | oai:riunet.upv.es:10251/145163 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/145163 |
| Access Level: | acceso abierto |
| Palabra clave: | Fortifications Mediterranean Modern age Built Heritage |
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Il pentagono come strumento per il disegno delle fortezzeMagnaghi-Delfino, PaolaMele, GiampieroNorando, TulliaFortificationsMediterraneanModern ageBuilt Heritage[EN] 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.Editorial Universitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20202020-05-15book parthttp://purl.org/coar/resource_type/c_3248VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/bookPartapplication/pdfhttps://riunet.upv.es/handle/10251/145163reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Italianoitaopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1451632026-06-13T07:49:27Z |
| dc.title.none.fl_str_mv |
Il pentagono come strumento per il disegno delle fortezze |
| title |
Il pentagono come strumento per il disegno delle fortezze |
| spellingShingle |
Il pentagono come strumento per il disegno delle fortezze Magnaghi-Delfino, Paola Fortifications Mediterranean Modern age Built Heritage |
| title_short |
Il pentagono come strumento per il disegno delle fortezze |
| title_full |
Il pentagono come strumento per il disegno delle fortezze |
| title_fullStr |
Il pentagono come strumento per il disegno delle fortezze |
| title_full_unstemmed |
Il pentagono come strumento per il disegno delle fortezze |
| title_sort |
Il pentagono come strumento per il disegno delle fortezze |
| dc.creator.none.fl_str_mv |
Magnaghi-Delfino, Paola Mele, Giampiero Norando, Tullia |
| author |
Magnaghi-Delfino, Paola |
| author_facet |
Magnaghi-Delfino, Paola Mele, Giampiero Norando, Tullia |
| author_role |
author |
| author2 |
Mele, Giampiero Norando, Tullia |
| author2_role |
author author |
| dc.contributor.none.fl_str_mv |
Repositorio Institucional de la Universitat Politècnica de València Riunet |
| dc.subject.none.fl_str_mv |
Fortifications Mediterranean Modern age Built Heritage |
| topic |
Fortifications Mediterranean Modern age Built Heritage |
| description |
[EN] 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. |
| publishDate |
2020 |
| dc.date.none.fl_str_mv |
2020 2020-05-15 |
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book part http://purl.org/coar/resource_type/c_3248 VoR http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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info:eu-repo/semantics/bookPart |
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bookPart |
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https://riunet.upv.es/handle/10251/145163 |
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https://riunet.upv.es/handle/10251/145163 |
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Italiano ita |
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Italiano |
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ita |
| dc.rights.none.fl_str_mv |
open access http://purl.org/coar/access_right/c_abf2 Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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info:eu-repo/semantics/openAccess |
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open access http://purl.org/coar/access_right/c_abf2 Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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application/pdf |
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Editorial Universitat Politècnica de València |
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Editorial Universitat Politècnica de València |
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reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname:Universitat Politècnica de València (UPV) |
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Universitat Politècnica de València (UPV) |
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RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
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RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
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