Geometría y traza de escaleras góticas. Las escuadras como ábacos en la construcción de los caracoles de la catedral de Tortosa

• Published in: Informes de la construcción 2016, Vol.68 (541), p.e132-e132
• Main Author: Lluis i Ginovart, J.
• Format: Article
• Language: eng ; spa
• Subjects: Arithmetic; catedral tortosa; Cathedrals; Circumferences; Division; escuadras; geometría medieval; Gothic period; Legs; Polygons; polígonos regulares; Staircases; tratados históricos
• ISSN: 0020-0883; 1988-3234
• DOI: 10.3989/ic.15.035

In the Gothic era, spiral staircases were one of the greatest showpieces of the magister operis knowledge. They were the focus of arithmetic and geometric medieval constructor knowledge. Their construction involved the use of templates known as gabarits, which required the polygonal division of the circumference. These regular 11-, 13-, 14-, 17- and 19-sided polygons do not appear in the Euclid’s Elementa or the Tolomeo’s Almagest, or in the few Practica Geometriae of the time. These polygons can be constructed by using a square with two arms, supporting repeatedly the legs on the hypotenuse, a rotation of the instrument. Squares constructed using arithmetic or geometric methods must always be calibrated and can therefore be used as an abacus, which enables the circumference to be divided with sufficient accuracy. San Pedro (1383) and Santa Catalina staircases (1424), of Tortosa’s cathedral, have been drawn by the instruments explained previously.