Optics and Mathematics in the Domed Churches of Guarino Guarini

1991 ◽  
Vol 50 (4) ◽  
pp. 384-401 ◽  
Author(s):  
Elwin C. Robison
Keyword(s):  
Structural Theory ◽  
Complex Geometries ◽  
Architectural Theory ◽  
Conic Sections ◽  
Guarino Guarini ◽  
Gothic Architecture ◽  
And Mathematics

The architecture of Guarini is distinguished from that of his Roman contemporaries by the complex geometries of his forms and the use of conic sections in his vaults. The use of advanced geometries in his domed churches was prompted not by numeric or structural theory but by optic considerations. The development of forced perspective in his vault shapes and use of light were influenced by theories on aesthetics and optics that were debated while Guarini was in Paris. The parallels between Guarini's architectural theory and that of Claude Perrault, as well as Guarini's unique aesthetic assessment of Gothic architecture, suggest that he developed these ideas during his four-year stay in Paris.

scholarly journals Operationalism: An Interpretation of the Philosophy of Ancient Greek Geometry

2021 ◽  
Author(s):  
Viktor Blåsjö
Keyword(s):  
Good Reason ◽  
Diagrammatic Reasoning ◽  
Conic Section ◽  
Conic Sections ◽  
Ancient Greek ◽  
Classical Mathematics ◽  
And Mathematics ◽  
Reading Key ◽  
Made In ◽  
Greek Geometry

AbstractI present a systematic interpretation of the foundational purpose of constructions in ancient Greek geometry. I argue that Greek geometers were committed to an operationalist foundational program, according to which all of mathematics—including its entire ontology and epistemology—is based entirely on concrete physical constructions. On this reading, key foundational aspects of Greek geometry are analogous to core tenets of 20th-century operationalist/positivist/constructivist/intuitionist philosophy of science and mathematics. Operationalism provides coherent answers to a range of traditional philosophical problems regarding classical mathematics, such as the epistemic warrant and generality of diagrammatic reasoning, superposition, and the relation between constructivism and proof by contradiction. Alleged logical flaws in Euclid (implicit diagrammatic reasoning, superposition) can be interpreted as sound operationalist reasoning. Operationalism also provides a compelling philosophical motivation for the otherwise inexplicable Greek obsession with cube duplication, angle trisection, and circle quadrature. Operationalism makes coherent sense of numerous specific choices made in this tradition, and suggests new interpretations of several solutions to these problems. In particular, I argue that: Archytas’s cube duplication was originally a single-motion machine; Diocles’s cissoid was originally traced by a linkage device; Greek conic section theory was thoroughly constructive, based on the conic compass; in a few cases, string-based constructions of conic sections were used instead; pointwise constructions of curves were rejected in foundational contexts by Greek mathematicians, with good reason. Operationalism enables us to view the classical geometrical tradition as a more unified and philosophically aware enterprise than has hitherto been recognised.

scholarly journals The application models of the topological principle of continuous deformation in the architectural design process

2017 ◽  
Vol 15 (3) ◽  
pp. 453-464
Author(s):  
Maja Dragisic ◽  
Andjelka Bnin-Bninski
Keyword(s):  
Design Process ◽  
Architectural Design ◽  
Design Methodology ◽  
Architectural Theory ◽  
Architectural Discourse ◽  
Building Technology ◽  
Continuous Deformation ◽  
And Mathematics ◽  
Topological Principle ◽  
Structural Aspects

Architecture and geometry share a mutual history, and their relationship precedes the introduction of digital and computer technologies in architectural theory and design. Geometry has always been directly related to the modalities of thinking in architecture through the problems of conceptualisation, representation, building, technology. Through the historical overview of these two disciplines, it is possible to perceive direct influences of geometry on the architectural creative concepts, formal characteristics of architectural works, structural aspects, and building methods in architecture. However, the focus of this paper is not on the representation of historical intertwining of these two disciplines, which is indisputable, it is on the attempt to represent one specific bond between topology and architecture, firstly through the explanation of the principle of continuous deformability, and secondly through the representation of the models through which the principle occurs in the architectural design process, as well. The first part of this work will introduce and analyse the transition of concepts of continuity and deformability, from mathematical topology through philosophy to architecture, while the second part of the work will explain two models in detail, formal and systematic, through which the principle of continuous deformation is applied in certain architectural design practices. Overall, this work deals with the interpretation of the principle of continuous deformation in architecture and it shows in which way the architectural discourse changes the meaning of a mathematical-philosophical notion and turns it into a design methodology of its own. The subtlety of the question Bernard Tschumi asks about space illustrates the need to thoroughly investigate interdisciplinary relation between architecture, philosophy, and mathematics: ?Is topology a mental construction toward a theory of space?? (Tschumi, 2004, p.49)

scholarly journals “Ars sine scientia” or rather “Ars sine geometria”? The debate of 1400 on the elevation of Milan cathedral

2019 ◽  
Vol 2 (3) ◽  
pp. 65
Author(s):  
Giulia Ceriani Sebregondi
Keyword(s):  
Architectural Theory ◽  
Building Site ◽  
Gothic Architecture ◽  
Sacred Architecture ◽  
Architecture And Literature ◽  
History Of ◽  
The One ◽  
The Relationship ◽  
James Ackerman ◽  
European Architecture

The construction of Milan Cathedral from 1386 was one of the most important episodes in the history of Italian and European architecture because of the uniqueness of the building itself — the largest Gothic church ever constructed in Italy — and because of the presence of some of the most authoritative architects of the late Fourteenth and Fifteenth centuries in Europe (Lombard, French, German).The documentation about the discussions on how to build the Duomo in the late Trecento and early Quattrocento, especially on the structural choices to be made and the different Lombard and Northern building-site practices, made famous to English readers in a celebrated article by James Ackerman, is extraordinarily rich and extensive, permitting considerations on the relationship between medieval architectural ideals and an actual project.The paper focuses on the famous discussions of 1400, in part a re-run of those of 1392. It will be argued that famous criticism by the French expert Jean Mignot of Milanese architects involving the terms ars and scientia could have a very different meaning from the one generally accepted in the literature. Consequently, it will result that Mignot wanted to return to the original project proposed by Gabriele Stornaloco, which embodied the desired correspondence between the sacred architecture and the perfect God’s world.All of which, could be of some interest to medievalists in general, and to those concerned with architectural theory and with the relationship between Gothic architecture and literature in particular.

scholarly journals Tas-de-charge – An Essential Part of Gothic Vault

2021 ◽  
Author(s):  
Krisztina Fehér
Keyword(s):  
Architectural Theory ◽  
Medieval Architecture ◽  
Gothic Architecture ◽  
Multiple Loads ◽  
Empirical Learning ◽  
Dynamic Development ◽  
Stone Block ◽  
Particular Solution ◽  
The Creation ◽  
Architectural Knowledge

Gothic architecture can be viewed from several perspectives, including stylistic aspects, architectural theory, and structural analysis.As Gothic architecture is a skeletal construction, it is essential to achieve an equilibrium with the multiple loads and forces. Medieval master masons' architectural knowledge was firmly based on empirical learning, which stimulated the dynamic development of structural innovations.This paper emphasises and describes a particular type of vault springer, one of the most complicated and sensitive parts of Gothic construction. Known as tas-de-charge, it became especially characteristic of high Gothic architecture. According to its principle, the springer's lower courses contain the merged vault nerves and are carved from one single stone block in each course. The beds of these courses are not radial as those of the average voussoirs, but horizontal. Without the concept of tas-de-charge, the development of late Gothic vaults could not be imaginable. This particular solution made possible the creation of elegantly narrow imposts supporting the vault ribs, the double arch and the formerets. So far, tas-de-charge has not been a focus of interest in the historiography of Hungarian medieval architecture; however, it appears that it was commonly applied in our late Romanesque and early Gothic monuments.

Stauffer Cathedral: A Post-Modern Library

2017 ◽  
Author(s):  
Elizabeth Cai
Keyword(s):  
Architectural Theory ◽  
Innovative Design ◽  
Gothic Architecture ◽  
Modern Library ◽  
Interior Spaces ◽  
History Of ◽  
Queen's University

Completed in October 1994, the Joseph S. Stauffer Library is undoubtedly an audacious new addition to the landscape of Queen's University. Its innovative design, coupled with the library's emphasis on electronicbased learning, distinguishes the building as a product of the contemporary period. When examining the structure's aesthetic elements, however, its skeletal exterior frame, lofty interior spaces, and rising vertical supports recall the tenants of a much older tradition – those of Gothic architecture. This paper will examine the use of post-modern architectural theory by the library's architects and the homage paid to Gothic architectural traditions in order to place Stauffer Library in the long history of collegiate architecture.

scholarly journals Jantzen and Sedlmayr: Diaphaneia—an impossible presence?

2019 ◽  
Author(s):  
Stepan Vaneyan
Keyword(s):  
James Joyce ◽  
Visual Experience ◽  
Architectural Theory ◽  
Gothic Architecture ◽  
Gothic Cathedral ◽  
Bodily Presence ◽  
Pierre Teilhard De Chardin ◽  
Ultimate Question ◽  
Per Se ◽  
Seminal Article

The immediacy of visual experience has always appeared as an indicator of verifiability of a presence. However, architecture as a bodily presence seems to be a reality that does not need verification. Yet there remains the issue of sacral architecture, which strives for the transcendent. What can be a medium in the experience of theophany? Sacral experience of Gothic architecture is very suitable for such observations. However, as I hope to demonstrate, only one theory seems to have actually approached the understanding of interconnections between the Holy Presence and the experience of it on an architectonic level. Precisely, it is Hans Jantzen’s (1881-1967) programmatic theory of “a diaphanic structure”. Term “diaphaneia” was first introduced by Jantzen in his article “Über den gotischen Kirchenraum” (1927). By that time the word had been used in near-esoteric circles (from Jacob Boehme to Pierre Teilhard de Chardin and James Joyce).  Jantzen’s seminal article is dedicated to the space of the Gothic cathedral, which he sees as ritual-liturgical. It is this multilayered space, he argues, that has a “diaphanic structure”. In his late texts (from the 1950 and 1960s) diaphaneia is explored as a universal way of keeping in view the horizon of the invisible presence. Sedlmayr's perception of Jantzen's ideas shows that optical diaphaneia should be complemented with somatic diaphaneia  (through “baldachin”, in Sedlmayr's structuralist terms). The ultimate question is if diaphaneia is merely a means of “spiritualisation” of both the cathedral per se and architectural theory. Although architecture keeps silent, an architectural theorist speaks: using Derrida’s words, diaphaneia becomes diaphonie.

Models and mathematics. Tools of the mathematical biologist

JAMA ◽  
1965 ◽  
Vol 194 (3) ◽  
pp. 269-272
Author(s):  
J. T. Apter
Keyword(s):  
And Mathematics
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