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2010 | Book

Letter From The Editor Read chapter Read first chapter

Architecture, Mathematics and Perspective

Editor: Tomás García-Salgado

Publisher: Birkhäuser Basel

Book Series : Nexus Network Journal

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Table of Contents

Frontmatter

Letter From The Editor

Letter From The Editor
Tomás García-Salgado

Architecture, Mathematics and Perspective

Giotto and Renaissance Perspective
Abstract
A careful geometric examination of the blind arcades ( coretti) depicted in Giotto’s fresco on the choir wall in the Arena Chapel in Padua shows that they were designed and painted according to the rules of what I term “progressive costruzione legittima” and thus represent simulations of visual images. Because no images of this type have come down from Classical Antiquity and because the literary references remain silent in this respect, the coretti must be considered, according to today’s knowledge, the oldest monuments manifesting the application of the costruzione legittima. This means the history of the central (linear) perspective must be rewritten. In any case it was not a Renaissance invention. I expressly agree with the researchers who see Giotto’s painting in conjunction with the findings of the Scholastic “optics specialists” (such as Grosseteste, Witelo, Bacon), who all stood with their feet firmly planted on the ground of Euclid’s rigidly geometrically conceived visual theory and its Arab commentators.
Volker Hoffmann
Perspective, a Visionary Process: The Main Generative Road for Crossing Dimensions
Abstract
Perspective is the only tool able to create subjective links between human beings and art spaces. Each perspective representation can be drawn only by identifying a subjective point of view, which varies from individual to individual. This represents a subjective way of interpreting the hidden logical structure of the world. By interpreting the “perspective” representations of the artists of our past we can approach their cultural visions through a possible re-constructing of their represented spaces, a non-linear process that opens a creativegenerative path from past to future, teaching us that “dolce” perspective is the main road for our logical interpretation of art. Starting in 1979 I designed original software for space representations. My investigations concerned perspective and, in general, representations crossing multiple dimensions.
Celestino Soddu
Perspective in a box
Abstract
Perspective is an optional subject for students of some levels in Dutch secondary schools. A proper final task on this subject is the analysis of existing perspective drawings or paintings. This task is sometimes supplemented by a more creative and challenging assignment, that is, the design and construction of a perspective box. A perspective box is an empty box with, on the inner sides, perspective pictures giving a surprising spatial effect when observed through the peephole. The students who take up the challenge are in the first place inspired by the six still existing antique wooden perspective boxes, especially because they were created by Dutch seventeenth-century painters of architecture and interiors. In this article the setup of the perspective in these boxes will be discussed. But for a clear comprehension, we begin by reviewing the principles of linear perspective and their implications for the way perspective images can best be viewed.
Agnes Verweij
Juan Bautista Villalpando and the Nature and Science of Architectural Drawing
Abstract
In 1604, Jesuit priest and architect Juan Bautista Villalpando published In Ezechielem Explanationes, a massive three-volume scriptural exegesis on the Book of Ezekiel. Volume Two was dedicated to the reconstruction of Ezekiel’s vision of the Temple of Solomon and consists of five books: on the prophecy on the Temple; its plan and reconstruction; the justification of the reconstruction; its bronzes and ornamentation, and an entire book on the nature and science of architectural drawing. Initially the latter appears out of place in a Scriptural exegesis but he explained that the purpose of this book was to provide a guide for theologians so that they can form a mental idea or image of Temple, for their understanding and enlightenment of the entire Temple. However, throughout the text he points to the utility of the book to architects. For Villalpando the laws of optics were essential to the norms of perspective. Moreover, the sense and structure of seeing was a crucial element to the norms of mathematic and architecture, it is also a central theme in his theology. This paper examines his theory and his proposal of perspective for architecture drawing.
Tessa Morrison
Perspective versus Stereotomy: From Quattrocento Polyhedral Rings to Sixteenth-Century Spanish Torus Vaults
Abstract
Quattrocento perspective and Spanish sixteenth-century stereotomy share a number of concepts, problems and methods, although there seems to be no direct substantial connection between them. This suggests the existence of a common source, but it is not easy to identify it. Neither classical geometry nor the mediaeval practical geometry tradition include a word about orthographic projections, rotations or projection planes. Thus, mediaeval construction shop practices furnish the most probable common source for perspectival and stereotomic methods. Curiously, these practices are seldom mentioned in the exhaustive literature on perspective; even the use of orthogonal projection, although impossible to deny, is not often stressed. On the other side, Gothic tradition is recognised, at least in Spain, as an important source of Renaissance stereotomic methods. By contrast, the role of perspective and Italian and Italianate artists, which has been downplayed so far, should also be taken into account as a source of Renaissance stereotomy.
José Calvo-López, Miguel ángel Alonso-Rodríguez
The Sunlight Effect of the Kukulcán Pyramid or The History of a Line
Abstract
When the sunlight bathes the Kukulcán Pyramid in the Mayan city of Chichén-Itzá during the equinox sunset, it casts seven triangles of light and shadow that creep downwards along its northeast stairway. According to the Popol Vuh, the effect can be interpreted as the myth of the gods of the Heart of Sky coming to the Sovereign Plumed Serpent. Unfortunately, neither the event nor the kind of geometry used to build the pyramid is reported in the extant Mayan codices. There are two reliable facts: first, a line across the pyramid’s base coincides with the orientation of the summer-winter solstice; second, an earlier, smaller pyramid is concealed beneath the current one. Hence the major question here is whether the light and shadow effect was intended or occurs accidentally. Perspective as a surveying method for building provides a key to this riddle, because it accounts for a line according to which the Kukulcán Pyramid was built. To tell the history of this line, we have to bring into context other sunlight effects that take place across the Mayan area, taking into account the question of how the buildings in which such effects occur were built.
Tomás García-Salgado
Some Adaptations of Relativity in the 1920s and the Birth of Abstract Architecture
Abstract
John Hatch examines the friendship between Theo Van Doesburg and El Lissitzky, which was fuelled by a shared interest in scientific theories. Both moved from painting to architecture in seeking out a form best suited to conveying the spatiotemporal experiences phrased by Relativity, resulting in some remarkably innovative architectural designs and theories.
John G. Hatch

Book Reviews

The Mirror, the Window, and the Telescope: How Renaissance Linear Perspective Changed Our Vision of the Universe
Samuel Y. Edgerton
The Geometry of an Art. The History of Perspective from Alberti to Monge
Kirsti Andersen
Forma y Representación. Un Análisis Geométrico
Javier Navarro de Zuvillaga
Backmatter
Metadata
Title
Architecture, Mathematics and Perspective
Editor
Tomás García-Salgado
Copyright Year
2010
Publisher
Birkhäuser Basel
Electronic ISBN
978-3-0346-0518-2
Print ISBN
978-3-0346-0517-5
DOI
https://doi.org/10.1007/978-3-0346-0518-2

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