Proceedings
Nexus Ph.D. Day
Relationships between
Architecture and Mathematics
and Poster Session
Politecnico di Milano
11-14 June 2012
D I PA R T I M E N T O
IN DACO
D I PA R T I M E N T O D I
M AT E M AT I C A
edited by Michela Rossi
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Nexus 2012
Relationships between Architecture and Mathematics
Politecnico di Milano 11-14 June 2012
D I PA R T I M E N T O
INDACO
D I PA R T I M E N T O D I
M AT E M AT I C A
Nexus: Relationships between Architecture and Mathematics
1996 - Fucecchio (Florence) Italy
1998 - Mantua, Italy
2000 - Ferrara, Italy
2002 - Óbidos, Portugal
2004 - Mexico City, Mexico
2006 - Genoa, Italy
2008 - San Diego, California, USA
2010 - Porto, Portugal
2012 - Milan, Italy
The Nexus conferences were created by Kim Williams, with the first edition held in 1996, with Nexus ’96 held in
Fucecchio (Florence) Italy, sponsored by the Fondazione Montanelli-Bassi, under the direction of Kim Williams.
The second conference, Nexus ’98, took place in Mantua, Italy, under the auspices of the Accademia Nazionale
Virgiliana and the Centro Studi Leon Battista Alberti di Mantua, directed by Kim Williams and Livio Volpi Ghirardini. It was at the second conference that the decision was made to begin the Nexus Network Journal. The
founding of the NNJ made possible communication and diffusion of research between the biennial Nexus conferences. Nexus 2000 took place in Ferrara, Italy, directed by Kim Williams, with the support of the Dipartimento
di Matematica and the Dipartimento di Architettura of the University of Ferrara. It was at this conference that the
first Round Table Discussion was held, providing an important forum for interdisciplinary discussion. Nexus 2002
was held in Óbidos, Portugal, sponsored by the Centro de Matemáteca e Aplicações Fundamentais (CMAF) of
the University of Lisbon. Co-directed by Kim Williams and José Francisco Rodrigues, it was the first Nexus conference held outside Italy. Nexus 2004, co-directed by Kim Williams and Francisco Delgado Cepeda, took place in
Mexico City, with the support of the Instituto Tecnolólogico de Estudios Superiores de Monterrey, Campus Estado
de México. Nexus returned to Italy with Nexus 2006 in Genoa, co-directed by Kim Williams, Orietta Pedemonte
and Sylvie Duvernoy, sponsored by the Dipartimento per la Scienza dell’Architettura of the University of Genova.
Nexus 2008 was hosted by Point Loma Nazarene University in San Diego, California, and was co-directed by
Kim Williams, Maria Zack, and Sylvie Duvernoy. The 2010 edition of Nexus took place in June 2010 in Porto,
Portugal, sponsored by the Faculty of Sciences, the Faculty of Architecture, and the Centro de Matemáteca of the
University of Porto and the FCT – Fondação para a Ciência e a Tecnologia, and was co-directed by Kim Williams,
João Pedro Xavier, and João Nunes Tavares.
The aim of the Nexus Conferences
There are many connections between architecture and mathematics: mathematic principles may be used as a
basis for an architectural design, or as a tool for analyzing an existing monument; architecture may be a concrete
expression of mathematical ideas, becoming, in a sense, “visual mathematics”. The purpose of the Nexus conference series is to bring together all those working with ideas related to both architecture and mathematics, and to
allow researchers to exchange ideas first-hand. Papers presented at the conference are subsequently published,
providing a permanent archive of studies in architecture and mathematics.
The Nexus Network Journal
The NNJ is a peer-reviewed research resource for studies in architecture and mathematics published three times
a year in print by Kim Williams Books and Birkhäuser Publishers and is available online at SpringerLink. In 2010
the NNJ was accepted into the Thomson-Reuters ISI database. The purpose of the NNJ is to publish research
in architecture and mathematics that present the subject in the widest possible panorama. Thus, like the Nexus
conferences, the NNJ is interdisciplinary and multicultural. Topics explored include proportion, geometry, algebra,
topology, symbolism, fuzzy logic, complexity theory, fractals and chaos, tessellation, modularity, perspective,
metrology, symmetry, music, astronomy, construction history and mechanics, and the application of these in
architecture, landscape architecture and urban planning in all cultures and all epochs.
www.nexusjournal.com
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Nexus 2012 at Politecnico di Milano
Nexus 2012, the 9th edition of the International Conference Nexus: Relationships between Architecture and
Mathematics, takes place in Milan in 11-13 June 2012, hosted by Politecnico di Milano at Campus Bovisa. It is
sponsored by the Department of Industrial Design, Arts, Communication and Fashion and by the Department
of Mathematics. The peer review received the abstracts of 144 submitters from 28 country, many of which were
invited to submit a full paper for the further selection of the conference sessions, where only a few lectures can
be presented by the the authors. Oral presentation are published in the Nexus Network Journal.
Scientific committee:
Kim Williams, NexusNetworkJournal, director
Franca Caliò, Politecnico di Milano
Sylvie Duvernoy, Università di Firenze
Giulio Magli, Politecnico di Milano
Elena Marchetti, Politecnico di Milano
Michela Rossi, Politecnico di Milano
Rossella Salerno, Politecnico di Milano
Vasco Zara, Université de Bourgogne
Sessions and lectures:
Design from antiquity to the future
Michael Ytterberg, “The Dance in the Labyrinth: The Hidden Order of Hadrian’s Villa and the Order of
Modern Architecture”
Benjamin Ibarra Sevilla, “The Hidden Face of the Vault: Unveiling the Expression of the Avant-Garde through
the Use of the Sphere in Teposolula’s Open Chapel”
Jiang Liang, Yan-qui Hu, Hui San, “The Design Evaluation of Green Space Elements of Urban Squares
Based on Fractal Theory”
Silvia Benvenuti, Fabio Ceccanti, Xavier De Kestelier, “Living on the Moon: Topological Optimization of a
3D-Printed Lunar Shelter”
Music, Architecture and Mathematics
Radoslav Zuk, “Three Musical Interpretations of Le Corbusier’s Modulor”
Michela Costantini, “Signs of the Eighteenth-Century Debate on the Harmonic Theory in Piedmont”
Design and Representation analysis
Michael Ostwald, Michael Dawes, “Differentiating Between Line and Point Maps Using Spatial Experience:
Richard Neutra’s Lovell House”
Eliana Manuel Pinho, Joao Pedro Xavier, “Grid-Based Design in Roman Villas: A Method of Analysis”
Branko Mitrović, “Nelson Goodman’s Arguments against Perspective”
Parametric Design
Arzu Gonenc Sorguc, Semra Arslan Selcuk, “Computational Models in Architecture: Understanding MultiDimensionality and Mapping”
Stefano Converso, “Mathematics for the Design of Variation: The ‘Nagashima’ Lamp Prototype”
Rodrigo Garcia Alvarado, “Parametric Development of Variable Roof Structures with Central Supports
(Tulips)”
Cornelie Leopold, “Precise Experiments: Relations between Mathematics, Philosophy and Design at Ulm
School of Design”
Archaeoastronomy, Architecture and Mathematics
Michael A. Rappenglück, “The Housing of the World: About the Significance of Cosmographic Concepts for
Habitation”
Marina De Franceschini, Giuseppe Veneziano, Mario Codebò, “Architecture and Archaeoastronomy in
Hadrian’s Villa near Tivoli, Rome”
Javier Mejuto, “Astronomical Architecture and Landscape Modification in Prehistoric Iberian Peninsula”
Manuela Incerti, “Astronomical Knowledge in the Sacred Architecture of the Middle Ages in Italy”
Mathematics in architectural surfaces
Michele Emmer, “Minimal Surfaces and Architecture: New Forms”
Andrea Casale, Graziano Mario Valenti, Michele Calvano, Jessica Romor, “Surfaces: Concept, Design,
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Parametric Modeling and Prototyping”
Dmitri Kozlov, “Structures of Periodical Knots and Links as Geometric models of Complex Surfaces for
Designing”
Nicole Blanc, Bernard Parzysz, “How Archaeology and Mathematics Contributed to Say Something about a
Puzzling Set of Stucco Ceiling Coffers from Portici”
Keynote lectures
Fulvio Irace, Anna Chiara Cimoli, “Triennale 1951: Post-War Reconstruction and ‘Divina Proportione’”
Helmut Pottmann, “Geometric Computing for Freeform Architecture”
Alfio Quarteroni, “Mathematical models for simulation and optimal design”
Robert Hannah, “Greek Temple Orientation: The Case of the Older Parthenon in Athens”
The Nexus logo (2012)
The Logo design contains an architectural object, a mathematical object and a relation between the two. It
also contains information about “What”, “Where” and “When” incorporated into the graphic part rather than in a
separate text.
The Milan Cathedral was chosen to represent the architectural object for several obvious reasons:
being one of the symbols of Milan it signifies the place of the conference;
as a recognizable Gothic building it exemplifies the use of mathematics in both the tectonics and the
proportions of Gothic architecture and architecture in general;
the Cathedral was analyzed by the Milanese Architect and Geometer Cesare Cesariano in the early
16th Century, “apparently the first precisely measured illustrations of Gothic architecture in a printed
book”.
The Pascal Triangle was selected for the following reasons.
It is a constructed object as architectural objects are.
It exhibits interesting mathematical properties.
Its visual shape relates to one of the basic elements in the Cesare Cesariano’s analysis.
The Triangle hides the Fibonacci series and, therefore, the Golden Ratio, the same way buildings hide invisible
relations; it contains, with a slight modification, the dates of the conference.
The Logo has two versions, a “Dark” one and a “Light” one.
Ivan Mechkunov
“I am an architect, currently living in Ruse, Bulgaria after many years of study and work in the US. I have a Master’s from UT Austin and an unfinished PhD from UM Ann Arbor. In Ann Arbor my old love of Math was rejuvenated and under the guidance of late prof. Manos Vakalo I took a few Graph theory/Combinatorics and Computer
Science courses. I still live with the dream to produce some theoretical work, dedicated to the use of math and
logic in architectural design. My curiosity in that area led me to your journal, site and the logo competition.”
contact: [email protected]
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Scuola di Dottorato di Ricerca del Politecnico di Milano
School of Doctoral Programmes, Politecnico di Milano
Politecnico di Milano (POLIMI) is a state university established in 1863. It is organized in 16 departments and a
network of 9 Schools of Engineering, Architecture and Industrial Design.
POLIMI is the largest institution in Italy for Engineering, Architecture and Industrial Design with about 40.000
students enrolled. POLIMI is widely recognized for excellence in several research areas.
QS World University Rankings by Subject – “Engineering and Technology 2011-2012” ranks Politecnico di Milano
at the 48th place among the 300 eva- luated universities. Politecnico di Milano is the first Italian University ranked
among the best 50 technical universities in the world.
The Doctoral Programmes of Politecnico di Milano aim to develop the professional competence to carry out high
level research in manufacturing and service companies, public bodies and universities. The School of Doctoral
Programmes coordinates the Doctoral Degree Programmes of Politecnico di Milano in the areas of engineering,
architecture and industrial design.
The Doctoral Programs provide a selected number highly qualified graduates, endowed with a solid preparation
and keen intellectual curiosity, with the opportunity of acquiring a high degree of professional expertise in specific
scientific, technological, social and economic fields.
Ph.D. graduates are not only capable of carrying out research projects but develop, during their period of study,
new knowledge on scientific frontiers that can be immediately applied in professional activities.
Doctoral Programmes:
-
Interior Architecture and Design
Architecture, Urban Design, Conservation of Housing and Landscape
Bioengineering
Industrial Chemistry and Chemical Engineering
Architectural Composition
Preservation of Architectural Heritage
Design
Physics
Territorial Design and Government
Aerospace Engineering
Environmental and Infrastructure Engineering
Materials Engineering
Building Engineering
Information Technology
Electrical Engineering
Management, Economics and Industrial Engineering
Mechanical Engineering
Structural Seismic and Geotechnical Engineering
Mathematical Models and Methods in Engineering
Urban and Architectural Design
Design and Technologies Exploitation for the Cultural Heritage
Energetic and Nuclear Science and Technology
Spatial Planning and Urban Development
Technology and Design for Environment and Building
School Direction
director: Prof. Barbara Pernici
board: Prof. Paolo Biscari, Prof. Maria Gabriella Signorini, Prof. Ilaria Pamela Simonetta Valente,
Prof. Mariagrazia Folli
secretary: Mrs. Anna Lisa Riccardi
School of Doctoral Programmess:
Piazza Leonardo da Vinci 26, 20133 Milano
phone: +39 02 2399 9786
Fax: +39 02 2399 9700
e-mail: [email protected]
www.ricerca.polimi.it
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