Mathematical Beauty in Rome - A UCSD Global Seminar for Undergraduates
Mathematical Beauty in Rome 2009
A UCSD Global Seminar for Undergraduates
Joseph Pasquale
Professor of Computer Science
Dept. of Computer Science & Engineering
University of California, San Diego
pasquale@cs.ucsd.edu, 858 534-2673, http://www-cse.ucsd.edu/~pasquale
News
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Mathematical Beauty in Rome 2008
was unforgettable!
Here are some
photos
(more to come soon).
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Planning for
Mathematical Beauty in Rome 2009
is underway.
Sign up, as space is very limited!
Synopsis
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5 weeks during Summer Session 1 in Rome, Italy to study advanced topics in math, engineering, and architecture
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Seminar consists of two classes, and will be small, limited to 15-20 students
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The prerequisite is calculus/analytic geometry, either Math 10A/B/C or 20A/B/C,
and permission by the instructor
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For more info,
see the
UCSD Programs Abroad Office
or contact
Jenny Garza
The goal of this seminar,
which took place in Rome Italy in summer 2008
and will be offered again in summer 2009,
is to
explore classical Roman architecture
from a mathematical and engineering point of view.
We will study the geometries and structural principles of the Colosseum,
the Pantheon, St. Peter's basilica, Roman aqueducts, Roman bridges, and
much more. There will be excursions to Florence to study Brunelleschi's
dome and to Pisa to study the Leaning Tower. We will address such questions
as:
What geometrical forms were used, and why were they used?
How does a Roman arch work, and how is it analyzed for stability?
More generally,
what engineering principles enabled some of the world's greatest structures
to last for two millennia? These and other questions will be dealt with
in a mathematically rigorous manner.
Finally, we will live in and experience Rome, the "Eternal City,"
for five weeks.
This seminar is comprised of two courses:
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Mathematical Beauty in Rome (CSE 4GS)
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Mathematical Beauty in Rome - Lab (CSE 6GS)
The first course focuses on theoretical concepts in mathematics and engineering as they relate to classical Roman architecture.
We will explore basic structural principles of elements
such as arches, vaults, and domes,
and diverse mathematical topics such as the golden ratio and perspective.
The second course is a lab, comprising two activities: field study and computer analysis. Field study will involve visiting Rome's primary architectural sites to carry out observation and measurement studies. Computer analysis will involve use of software tools for geometric modeling and design analysis, and relating the measurement studies to the theory discussed in class.
Site-specific topics of study include the geometrical principles
of the Colosseum's oval design and the structural principles
of its multi-tiered arcaded design.
What are the properties of this oval, and how was it generated?
We will study the Pantheon, one of the best-preserved buildings of the
ancient world, which has a hemispheric dome with a central circular opening,
or "oculus." Why this geometry,
why the chosen dimensions,
and how were
they determined?
How was the dome erected?
The Colosseum (left) and the Pantheon (right):
actual views and geometric analyses.
Other studies under consideration include:
Michelangelo's dome at St. Peter's basilica
road engineering of the Appian Way
thermal design of the Baths of Caracalla
Rome's water distribution system
the Aqua Claudia aqueduct
Roman fountains, and how they work
the church of San Ignazio to study Pozzo's ceiling,
a masterpice of perspective
If you have a passion for mathematics (especially geometry) and
engineering, an appreciation for classical architecture,
and want to see these subjects come alive by studying
some of the greatest and most beautiful structures
ever built and that have stood the test of time,
on site,
this Global Seminar is for you!
Schedule
Each week, there will generally
be two days during which there will be classes,
two days of lab, and one day of an excursion outside of Rome.
The schedule of main sites in Rome and excursion sites are (tentatively):
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Orientation, tour of Rome, Castel Sant' Angelo
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Roman Forum, Roman temples
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Piazza Campidoglio, Museo Capitolini
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Aqua Claudia, Via Appia Antica, Baths of Caracalla
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Colosseum, Palatine Hill
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Museo Civilta Romana (EUR)
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Pantheon, Piazza Navona, Campo dei Fiori, Piazza Farnese
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Excursion: Ostia Antica
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Excursion: Florence
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Duomo and Brunelleschi's dome, Baptistry
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Santa Maria Novella, Santa Croce, Ufizzi, Accademia (David)
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Museo di Scienza (Galileo)
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Excursion: Pisa (Leaning tower, Duomo, Baptistry)
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St. Peter's basilica and Michelangelo's dome
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Opera at Terme di Caracalla
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Vatican museums, Sistine Chapel
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Excursion: Tivoli (Hadrian's Villa, Villa d'Este)
Pre-requisites
The main prerequisites are basic courses in mathematics,
i.e., calculus and analytic geometry (Math 10ABC or Math 20ABC). In addition, prospective students must
submit a one-page essay describing why they are interested in this Global
Seminar, and must meet with the instructor for permission.
If you are a student majoring in engineering (of any subdiscipline, e.g.,
computer science/engineering, structural engineering, etc.)
or mathematics, you are more than qualified to enroll.
If you are in doubt, please feel free to check with me.
Reading List
Selected readings from books
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De architectura,
by Vitruvius, 15 BC (Vitruvius: Ten Books on Architecture, ed. Ingrid D. Rowland Thomas Noble Howe. Cambridge University Press, 2001.)
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Principles of Roman Architecture, by Mark Wilson Jones. Yale University Press, 2003.
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Squaring the Circle: Geometry in Art and Architecture, by Paul Calter. Key College, 2008.
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Tutte l'opere d'architettura et prospetiva, by Serlio
(Sebastiano Serlio on Architecture, Volume 1: Books I-V, Translators: Vaughan Hart and Peter Hicks, Yale University Press, 2005)
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On the Art of Building in Ten Books, by Alberti
(Leon Battista Alberti On the Art of Building in Ten Books,
translated by J. Rykwert, N. Leach, R. Tavernor, MIT Press, 1988.
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Classical Architecture, by James Stevens Curl.
W. W. Norton and Co., 2001.
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Roman Architecture, by Frank Sear. Cornell University Press, 1983.
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The Stone Skeleton: Structural Engineering of Masonry Architecture, by Jacques Heyman. Cambridge University Press, 1995.
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Arches, Vaults and Buttresses, by Jacques Heyman, Variorum, 1996.
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Structural Analysis: A Historical Approach, by Jacques Heyman, Cambridge University Press, 1998.
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The Masonry Arch, by Jacques Heyman. Halsted Press (Wiley), 1982.
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The Colosseum, by Keith Hopkins and Mary Beard. Harvard University Press, 2005.
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Story of the Roman Amphitheatre, by D. L Bomgardner. Routledge, 2002.
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Roman Aqueducts and Water Supply, by A. Trevor Hodge. Duckworth Publishers, Second ed., 2002.
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Guide to the Aqueducts of Ancient Rome, by Peter J. Aicher. Bolchazy-Carducci Publishers, 1995.
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Brunelleschi: Studies of His Technology and Inventions, by Frank D. Prager and Gustina Scaglia. Dover Publications, 2004.
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Brunelleschi's Cupola: Past and Present of an Architectural Masterpiece, by Giovanni Fanelli and Michele Fanelli. Mandragora, 2006.
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Roman Builders: A Study in Architectural Process, by Rabun Taylor. Cambridge University Press, 2003.
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Roman Building: Materials and Techniques, by Jean-Pierr Adam. Routledge, 2003.
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Structures or Why things don't fall down, by J. E. Gordon, Da Capo, 1978.
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Roman Bridges, by Colin O'Connor, Cambridge University Press, 1994.
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Circle and Oval in the Square of Saint Peter's: Bernini's Art of Planning,
by Timoty K. Kitao.
New York University Press, 1974.
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Proportion: Science, Philosophy, Architecture, by Richard Padovan.
Spon Press, 1999.
Selected readings from journal and conference articles
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M. T. Bartoli, "Palazzo della Signoria in Florence: details and rules of Gothic architecture,"
Disegnare, idee e immagini, no. 29, Editore Gangemi, Roma (Dec. 2004), pp. 26-33.
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R. Corazzi and G. Conti, "Brunelleschi's dome between theory and reality,"
Disegnare, idee e immagini, no. 31, Gangemi Editore, Roma (Dec. 2005), pp. 56-67.
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"Il Colosseo Studi e Ricerche,"
Disegnare, idee e immagini, no. 18-19, Editore Gangemi, Roma (June/Dec 1999). (entire issue devoted to research on the Colosseum)
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M. Docci, "The architectural orders of the Colosseum,"
Disegnare, idee e immagini, no. 29, Editore Gangemi, Roma (Dec. 2004), pp. 26-33.
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S. Duvernoy and P. L. Rosin, "The Compass, the Ruler and the Computer", Proc. Nexus VI: Architecture and Mathematics, pp. 21-34, 2006.
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N. T. Gridgeman, "Elliptic Parallels," The Mathematics Teacher, 63, (1970), pp. 481-485.
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N. T. Gridgeman, "Quadarcs, St. Peter's and the Coloseum", The Mathematics Teacher, 63 (1970), pp. 209-215.
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M. Wilson Jones, "Designing Amphitheatres,"
MDAI(R), Mitteilungen des deutschen archäologischen Instituts, Römische Abteilun- Mayence 100 (1993), pp. 391-442.
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P. L. Rosin and E. Trucco, "The Amphitheatre Construction Problem", Incontro Internazionale di Studi Rileggere L'Antico, 2005.
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P. L. Rosin, "On Serlio's construction of ovals", Mathematical Intelligencer, vol. 23, no. 1, pp. 58-69, 2001.
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T. Thieme, "La geometria di Piazza San Pietro," Palladio, XXIII (1973), 129-144.
Evaluation
Projects
There will be a set of group projects involving carrying out measurement
studies at various sites, followed by geometrical and/or statistical analysis
and evaluation using computer software tools. Project presentations by each
of the groups will be given on the final day, and will be evaluated based on
content and presentation.
Final Exam
There will be a final exam, testing students on their understanding of the
readings, site visit studies, and material presented in class.
Last updated 9/1/08