Liliana CurcioIstituto statale d'arte per la progettazione della comunicazione visiva del disegno industriale e dell'ambiente Monza, via Boccaccio 1, Italy Versione
italiana We are happy to publish this
report, which appeared for the first time in Lettera Matematica Pristemno. 37, pp. 62-64, and is here reproduced with permission.
Mathematics and Architecture" was
the theme of the international conference Nexus
2000 (the proceedings of which, Nexus
III: Architecture and Mathematics, are already published),
held 4-7 June 2000 in Ferrara at the Musarc,
the National Museum of Architecture. This was the third edition
of the conference, organized by Kim Williams, and by now an established
biennial appointment for international scholars to discuss papers
that refer to relationships between mathematics and architecture.The presentations were inspired by diverse ideas, but were
in any case linked by a certainty: it is above all the intentions
(which then lead to certain decisions) that need to be made explicit,
especially when the research takes its point of departure from
an area that is apparently very far afield but which is then
brought to bear on themes related to the disciplines at hand.
It is in this context that in the course of the conference discussions
went from the analysis of the proportions of a Palladian villa
(in the presentation by Rachel
Fletcher) to the study of harmonic relations in the Cappella
dei Pazzi in Florence (presented by Mark
Reynolds). Further presentations went from interesting presentations
of eastern architecture, where the leading motive is the search
for the mathematic underpinnings of every kind of endeavor, to
the fascinating presentation of David
Speiser on Raphael's painting, Among the various presentations it is appropriate to mention those in which the link between architecture and mathematics lends itself to the teaching of mathematics. For example, Franca Caliò and Elena Marchetti presented a very valid experiment based on the creation of a virtual model through the use of a generative mathematical technique. The operative procedure consisted in observing the architectural object, extrapolating the geometric form that describes it, determining the mathematical equations of that form and then constructing the virtual model. Using a generative technique, the presenters explained, means singling out a base form to which is then applied a transformation, generally a linear transformation, through the use of matrices. It is clear that, in the decription of an architectural object, the models can be many and various; that which was presented was a model that, given the simplicity with which the curves were described, could easily be used in teaching an introductory course in mathematics in a faculty of architecture. The analysis of the model, and of the type of model in combination with the forms being considered, is a notable stimulus for the design process, both from and expressive-comunicative point of view and from a critical-operative point of view. These are two extreme relevant aspects for the acquisition of content and of methods of investigation, which obviously should be part of a didactic strategy at the university level. The Nexus conference closed with the presentation of Alessandra
Capanna, who recalled the emotions, sounds and history of
the project for the Philips Pavilion of Le Corbusier. In 1956
the architect was commissioned by the Philips corporation to
design a structure in which it was not necessary to exhibit any
of Philips' products, but which would be a demonstration of the
boldest effects of light and sound to illustrate what Philip's
technical progress might carry us in the future. This was in
effect a request for a symbol, a perennial image! The architect
accepted the commission, but his intention was to create a It is in this context that the Philips Pavilion lies, with
its futuristic form and its message comunicated through sound,
color and imagery. In the interior is the objet mathematique,
which justly recalls a polytope, the 24-cell, projected into
three-dimensional space. The introduction of the fourth dimension
- spatial and not temporal - not only into the imaginary space
but into the constructed space as well, is a bold and difficult
undertaking. The designed space is united with the abstract space
of mathematics, but "the variables of the constructed The wealth of emotions raised by each of the presentations, in a setting of great sympathy and amity, make Nexus a much-anticipated appointment. It is a moment in which to reflect profoundly on one's own daily work and an invaluable occasion both for comparing one's own ideas with those of scholars from other countries as well as transmitting the passion with which each individual research aims to come closer, and to bring us closer, to mathematics.
At the Musarc were displayed various didactic itineraries, as for example that of the polyhedra that comprise two models of polytopes - the 24-cell and the 120-cell - and that of the tilings of the plane with models of beautiful Italian pavements inspired by the work of Kim Williams. The exhibit also presented some interesting results of reflections on and analysis of works of great artists who measured themselves against the aesthetic and rational values of Geometry: from Ledoux to Le Corbusier, from Nervi to Calatrava, from Le Ricolais to Frei Otto and Fuller. The imposing model of the tetrahelix, at the center of the upper room, is emblematic of the research described. The form consists in a column - which theoretically could be reproduced to infinity - of regular tetrahedra joined in such a way so that each polyhedron wholly shares with two others a surface and with three others a vertex. The potential growth to the infinite is one of the most fascinating aspects of the tetrahelix. The search for beauty and harmony that permeates all the works exhibited is common to the history of all branches of knowledge , though with different canons and languages. Researchers of note have always been found in this field of enquiry. We recall only two, distant from each other in time but very close in terms of their aims. The first is Leon Battista Alberti, who held that beauty is the agreement and harmony of the parts in relation to a determined number just as the fundamental and most exact laws of nature require. The other researcher, already amply cited, is Le Corbusier who, in the third chapter of his book The Modulor says, "Mathematics is the majestic structure conceived by man to grant him comprehension of the universe…Harmony reigning over all things, regulating all the things of our lives, is the spontaneous, indefatigable and tenacious quest of man …pursuing one aim: to make a paradise on earth."[Le Corbusier, The Modulor, Basil, Birkhauser, 2000, p. 71-74] It is important to note that beauty and harmony are not the exclusive patrimony of a particular area, but are part of the culture and the research of all disciplines. Only by bringing all precepts, obviously each in its own specificity, to converge in the same direction, will it be possible to bring to light forms and typologies in a global consciousness that is truly innovative and lasting.
- Iannis Xenakis,
*Musica. Architettura,*Spirali Vel, 1976 (in Italian). - Iannis Xenakis,
*Musique. Architecture*(Paris, 1976). (in French). - Le Corbusier (Charles Edouard Jeanneret),
*The Modulor*and*Modulor 2.* - Kim Williams, ed.
*Nexus III: Architecture and Mathematics*, Pisa, Pacini Editore, 2000.
Lettera Matematica Pristem. She is
a coordinating member of the Centro Pristem of the Bocconi University,
Milan.
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