| The compass, the Straightedge and the Computer |
|---|
|
Department of Mathematics Milan Polytechic Piazza Leonardo da Vinci, 32 21033 Milan ITALY |
Department of Mathematics Milan Polytechic Piazza Leonardo da Vinci, 32 21033 Milan ITALY |
Studying
Arts and Architecture in connection with Mathematics to underline
important geometrical properties, we considered the Duomo of
Milan , one of the most important monuments in our city.
The construction of the Cathedral begun in the 1380s and continued, with delays, through the last century. Several different architects, artists and consultants (including Leonardo and Bramante) were asked to work on the design and to collaborate in the construction.
The Milan Cathedral, Gothic at the first glance, even if unusual, and completed by a Renaissance façade, looks to be complex but well-formed according to a proportioned superposition of different styles. Its majestic beauty conquers everyone, resident or non-resident alike, so as mathematicians, we tried to discover the secrets of that fascination in terms of aesthetic geometrical canons. Starting from the drawings by Cesare Cesariano (1475-1543), in which are evident ratios involving "metallic" numbers, we looked for different symmetries in the building, as well as in the decorative patterns of the floor and the stained-glass windows. In particular we analysed the arabesques in the coloured rose windows, each different from the others, but all described by dihedral or cyclic groups. The Duomo provided us with an opportunity to discover other mathematical peculiarities: meaningful curves in the inlaid marble decorations of the pavement and geometric figures in the windows recall forms even used in mechanical engineering.
Knowing of the wide cultural formation, at any given time,
of the architects, engineers and collaborators of the so-called
"Veneranda Fabbrica del Duomo" (venerable factory of
the Cathedral), we believe that such harmonic construction does
not arise by chance but is the natural synthesis of creativity
and technical and geometrical knowledge.
Figure: A rose window with cyclic symmetry
from the Cathedral of Milan. Photograph by Luisa Rossi Costa
and Elena Marchetti
About the authors
Elena Marchetti,
Associate Professor, has taught mathematics courses to architecture
students at the Faculty of Architecture of the Politecnico di
Milano since 1988. She has produced numerous publications in
Italian and international scientific journals in the area of
numerical integration. She has published many papers about the
applications of mathematics to architecture and arts. The experience
gained through intense years of teaching courses to architecture
students led her to collaborate in some books dedicated to this
topic, with multimedia support packages.
.
Luisa
Rossi Costa, Associate Professor of
Mathematical Analysis in the Engineering Faculties of the Politecnico
di Milano, developed researches in Numerical and in Functional
Analysis (the results are published in several papers). She contributed
also to the creation of the first-level degree in Engineering
via the Internet and of the e-learning platform M@thonline.
Since 1998, involved in the relationship between High Schools
and Politecnico, she wrote many papers in teaching methods, in
connection between Art, Architecture and Mathematics to familiarize
pupils with Mathematics, and collaborated in editing a book on
symmetry, complete of a DVD support.
.
|
Elena Marchetti and Luisa Rossi Costa, "What Geometries in Milan Cathedral?", pp. 63-76 in Nexus VI: Architecture and Mathematics, eds. Sylvie Duvernoy and Orietta Pedemonte Turin: Kim Williams Books, 2006. http://www.nexusjournal.com/conferences/N2006-MarRos.html |
|
|
|
