The Geometric Enigma of Small Baths at Hadrian’s Villa: Mixtilinear Plan Design and Complex Roofing Conception

Abstract

Starting in the late Domitian age, through Nero's Empire and ending in Hadrian's principate, an increasing technological shift relating to both opus caementicium and centring work made it possible to build cupolas with unprecedented technical solutions in terms of both dimension and shape. Hadrian's strain was applied to the development of innovative domes, as shown in various pavilions in his Tiburtine Villa and perfectly expressed by the well-known episode reported by Cassius Dio concerning the criticism expressed by Apollodorus of Damascus on the Emperor's ribbed vault design. Many researchers agree on the importance of the octagonal hall of the Villa's Small Baths in terms of its unusual shape and daring structure and on the significance of the access vestibule of the Piazza d'Oro. The geometry and construction knowledge suggested by their shapes make them perfect examples of the importance of mathematicians' influence on architects during the design process.

Composition and Shape of Hadrianic Domes

“…Cipriani et al (2017) proposed this interpretation scheme in line with the graphic hypothesis on the Octagonal Hall of the Domus Aurea by Lynne C.Lancaster (2005: 43).…”

“…To repeat the steps of the design process carried out by the original architect, a specific workflow had to be developed, based on the use of reverse modelling applications in combination with the hints from the limited amount of surviving technical literature regarding vaults and domes of the Roman world. Giangiacomo Martines (2015: 99-131); Conti and Martines 2010, Svenshon (2009) and Cipriani et al (2017) are among the works focussed on linking the results of accurate surveying techniques with the only existing ancient texts regarding design techniques for arches and vaults: they all refer to the seminal, but partially forgotten, Heronis Alexandrini, Opera quae supersunt omnia (Heiberg 1914), a comprehensive translation of and noteworthy commentary on the writings from the Greek mathematician. No one else could have approached the problem presented by these writings with the same awareness of Johan Ludvig Heiberg, who was able to handle the field of Greek and Latin literature as well as to deal with mathematics and engineering problems.…”

A graphical analysis of a skewed arched-masonry bridge along the Circumetnea railway track

“…Considering the goals of this research, the methodology developed is aimed at the rigorous verification of the geometry of the bridge using the investigation tools of the disciplines of surveying and representation as a system of interpretation and knowledge, from the real object to the designed shape [Santagati 2005;Cipriani et al 2017;Vitali 2017;Spallone et al 2019]. In this specific case, the study of the geometry and equipment of the vaults of oblique masonry bridges is a question linked to stereotomic tracing rules, solving a problem that in the past was treated bidimensionally by means of 3D modelling.…”

A Methodology for Planar Representation of Frescoed Oval Domes: Formulation and Testing on Pisa Cathedral

“…In the specific case of the Cathedral of Pisa, the shape of the plan at the impost height is oval; this feature makes this constitutive element incompatible with a revolved surface, as occurs in numerous previous examples, also belonging to the classical age, e.g., the Temple of Diana in Baia [11][12][13].…”