Oval Domes. The Case of the Basílica de la Virgen de los Desamparados of Valencia

[EN] The dome of the Basilica de la Virgen de los Desamparados of Valencia is an emblematic example of Valencian baroque architecture and painting. Its shape, oval or elliptical, has been the subject of controversy in various studies. The study of oval domes throughout history is a very interesting field of research because, among other things, the determination of the exact shape is important in order to conclude how it was built. We approach the problem from a new mathematical point of view, calculating the distances between the points that make up the real data cloud and the hypothetical form considered, oval or ellipse. The use of modern graphic surveying techniques, carried out with a 3D laser scanner, and computation with the powerful symbolic and numerical mathematical solver, Mathematica, has allowed us to accurately determine the shape of the dome and determine that its sections are not well-described by ellipses. A better fit is obtained assuming that sections are ovals. 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Oval Domes: History, Geometry and Mechanics

An oval dome may be defined as a dome whose plan or profile (or both) has an oval form. The word Aoval@ comes from the latin Aovum@, egg. Then, an oval dome has an egg-shaped geometry. The first buildings with oval plans were built without a predetermined form, just trying to close an space in the most economical form. Eventually, the geometry was defined by using arcs of circle with common tangents in the points of change of curvature. Later the oval acquired a more regular form with two axis of symmetry. Therefore, an “oval” may be defined as an egg-shaped form, doubly symmetric, constructed with arcs of circle; an oval needs a minimum of four centres, but it is possible also to build polycentric ovals. The above definition corresponds with the origin and the use of oval forms in building and may be applied without problem until, say, the XVIIIth century. Since then, the teaching of conics in the elementary courses of geometry made the cultivated people to define the oval as an approximation to the ellipse, an “imperfect ellipse”: an oval was, then, a curve formed with arcs of circles which tries to approximate to the ellipse of the same axes. As we shall see, the ellipse has very rarely been used in building. Finally, in modern geometrical textbooks an oval is defined as a smooth closed convex curve, a more general definition which embraces the two previous, but which is of no particular use in the study of the employment of oval forms in building. The present paper contains the following parts: 1) an outline the origin and application of the oval in historical architecture; 2) a discussion of the spatial geometry of oval domes, i. e., the different methods employed to trace them; 3) a brief exposition of the mechanics of oval arches and domes; and 4) a final discussion of the role of Geometry in oval arch and dome design

Design and analysis of cross vaults along history

The history of cross vaults began almost 2,000 years ago with a widespread use during the Middle Ages and Renaissance, becoming nowadays one of the most diffused and fascinating structural typologies of the European building cultural heritage. However, conversely to the undeniable excellence achieved by the ancient masons, the structural behavior of these elements is still at the center of the scientific debate. In this regard, with the aim of reviewing the knowledge on this subject as a concise and valuable support for researchers involved in conservation of historical buildings, with a focus on design rules and structural analysis, the present study firstly introduces the cross vaults from a historical perspective, by describing the evolution of the main geometrical shapes together with basic practical rules used to size them. Then, the article deals with the subsequent advancements in structural analysis methods of vaults, until the development of modern limit analysis.This work was partially carried out under the program "Dipartimento di Protezione Civile - Consorzio RELUIS", signed on 2013-12-27.info:eu-repo/semantics/publishedVersio

Cartographic Style in the First Urban Maps of Cadiz, Spain: A Technique in Transition

This article deals with the cartometric analysis of various seventeenth-century urban maps of the city of Cadiz (Spain), from among which the so-called Vista Arámburu and the map belonging to the atlas of the Marquis of Heliche, discovered in the Krigsarkivet (Military Archive) of Stockholm, stand out for their uniqueness. These hitherto relatively unknown documents present evidence of an evolution of cartographic style towards greater topographic accuracy and hence cannot just be considered as simple drawings. In this seventeenth-century period of transition, the cartography of the city evolved from sixteenth-century aerial-view perspectives to the exhaustive planimetric maps of the eighteenth century, made by Spanish and French Military Corps of Engineers. These documents hold great historical value, not only due to the importance of Cadiz during the Modern Age but also because these maps constitute a graphic testimony of the fortification and growth of the city in this period. © 2019 British Cartographic Society