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SIGMAAARTS

Resources for Math and Art Courses
This page is intended as a resource for those who want to design and teach a course in math and art. It contains responses from people who have taught such courses in the past and who responded to questions sent to SIGMAAARTS. The responses are listed; some include links to websites, names of books and the email addresses of those who have offered to provide more information.
Doris
Schattschneider:
There are several resources on the Mathematics and Art page for Math Awareness
Month, April 2003: http://www.mathaware.org/mam/03/
I designed and taught a Mathematics for Art and Design course for several
years , for art and design majors at Moravian College, and the course has
been continued (by Gordon Williams, and currently Kevin Hartshorn) since I
retired from teaching. It uses The Geometer's Sketchpad, many original notes
and activities, and resources drawn from books already mentioned as well as
"Connections" by Jay Kappraff and other sources. In addition to
material on symmetry (in two and three dimensions), polygons and polyhedra,
there is work with geometric constructions, similarity, ratio and proportion
(including its use in the representation of data, and its use as a composition
tool); special ratios such as the golden ratio are included. Other topics
that have sometimes been introduced are: projections on surfaces (including
linear perspective and anamorphosis) and fractals.
schattdo@MORAVIAN.EDU
Annalisa
Crannell:
If you're interested in perspective, Marc Frantz and I have a work in progress;
it's fairly close to being ready for publication. The main focus is perspective,
which is a subject of most introtodrawing courses (so there's real art involved);
there's also real math. We are currently expanding our materials into a text
and instructor's manual for Princeton University Press. Our deadline for submission
is next October, but the text is mostly done. It already contains materials
enough (in our experience and that of many others) for a onesemester course
in mathematics and art for liberal arts students. The latest (presentable)
version of the manuscript is in the directory http://php.indiana.edu/~mathart/vpbook/
and the file is called Viewpoints91806.pdf
You might also be interested in the file called DiscussionProblem4.pdf This
file discusses "Problem 4 of Lesson 4" which has now become problems 59
of Chapter 4 in the current manuscript. It's helpful to teachers who have
never assigned (or attempted!) perspective problems in a classroom setting.
Anyone who wants to is more than welcome to use these materials. All we ask
is that you give credit where appropriate, and please let us know how and
where you use them. Any comments or corrections would of course be welcome.
I hope you find these materials useful!
Dr. Annalisa Crannell
Faculty Don of South Ben House
Box 3003, Department of Mathematics
Franklin & Marshall College
Lancaster, PA 176043003
phone number: 7172914222
Joel Haack:
Another source is from the Mathematics Across the Curriculum Project at Dartmouth
College.
The website http://www.dartmouth.edu/~matc/math5.pattern/syllabus.html
still contains a
good deal of the material from a Pattern course taught in Spring 1996. It
has the advantage of containing both mathematics and art projects throughout.
Carol
Bier:
Check out my MICA students' work at
http://mathforum.org/geometry/rugs/resources/practicums/
Helmer
Aslaksen:
You may want to check out my course, Mathematics in Art and Architecture
http://www.math.nus.edu.sg/aslaksen/teaching/mathartarch.html
Helmer Aslaksen
Department of Mathematics National University of Singapore, Singapore 117543
Singapore
aslaksen@math.nus.edu.sg
www.math.nus.edu.sg/aslaksen/
Ruth Favro:
I have been teaching a mathart course called Geometry in Art for ~5 years,
having developed it for a Core requirement for the BA degrees in our College
of Architecture (design, imaging, interiors). It is populated by others as
well. There is a large range of math abilities in the course.
We do symmetry and groups first, with the study of the geometry of rigid motions
and tiling leading to the algebra of multiplication tables and group classification.
The next part is Fibonacci numbers and golden mean, Platonic and Archimedean
solids, and lastly perspective, with a nod at the end to using limits in finding
area and slope (our Core Curriculum states that the ideas of calculus should
be known to all, as one of the great contributions to society).
I use Symmetry, Shape, and Space by Kinsey and Moore (Key>College) but originally
used David Farmer's Symmetry & Groups (AMS) and many handouts. Also consider
parts of Heart of Mathematics (Key College). For perspective I use Marc Frantz
and Annalisa Crannell's notes from Viewpoints (coming out as a book), which
is at a very good level. All these are basically "discovery" learning materials.
We use Geometer's Sketchpad software.
I have a whole list of references which I will be happy to send if you are
interested, along with more details, such as projects and favorite internet
sites.
Prof. Ruth G. Favro
Mathematics & Computer Science Dept.
Lawrence Technological Univ.
Southfield, MI 48075
favro@ltu.edu
Lasse Savola:
I teach a similar course to Ruth's, entitled Geometry and the Art of Design,
at the Fashion Institute of Technology in New York City. My students are in
the school of art and design (fashion, interior, graphic, jewelry, toy, illustration,
etc.) and come with wide ranging mathematical backgrounds. The main emphasis
in my course is on symmetry. Group theory is introduced at a low level. We
also talk about tessellations, fractals, and Phi among other topics. I make
sure the students get to ANALYZE as well as CREATE every week.
I have been using the Symmetry, Shape and Space book for the past 6 years.
However, I have been creating my own materials for the online version of the
course that I have run for the past couple of years. I have begun using that
material for my facetoface classes as well. Perhaps my most interesting
selfmade materials are made with the Camtasia software.
Last semester I taught a Geometry and Art course at Reykjavik University in
Iceland. The students were mostly in the Mathematics Education program and
thus the slant was more towards mathematics. I made all the materials, mostly
problem sets, myself. The topics were as listed below:
Polygons, Tangrams
Regular and Semiregular Tilings
Polyominoes, Reptiles
Escher Tiles
Kites and Darts, Empires
Hyperbolic and Elliptic Geometry
Rosette Groups
Frieze Groups
Visualizations of Groups
Wallpaper Groups
Unit Cell in Planar Patterns
Golden Ratio
Ruler/Compass Constructions
Fractals, Mandelbrot Set
If anyone is interested in seeing any of the materials, please let me know.
savola@mindspring.com
Mike Hall:
I have been reading all of the talk regarding art and geometry. I created
a course titled "The Marriage of Art and Geometry" intended for high school
teachers of geometry and art. The content of the course is to illustrate all
of the content connections of geometry to art. It was a great class and I
would love to share some ideas with anyone interested.
Mike Hall Mike Hall ]
Assistant Professor of Mathematics
Arkansas State University
PO Box 70
State University, AR 72467
mike.hall@csm.astate.edu
Tony
Robbin:
So far all that's been mentioned for books for a math/art course or a math/humanities
course are far more math than art or culture. Please consider my book Shadows
of Reality, the Fourth Dimension in Relativity, Cubism, and Modern Thought.
(see link below) The book starts with a mathematical and cultural history
of the fourth dimension, beginning with Schlafli work in the 1850's, discusses
fantasies about the fourth dimension in popular literature of the 19th century,
how Picasso copied illustrations out of a 1903 math book for his portrait
of Kahnweiller, and how visualizations of fourdimensional figures were in
the back of Hermann Minkowski's mind in his formulation of special relativity.
The book continues to discuss a fourth geometric dimension for the construction
of Penrose patterns and quasicrystals in general. Current topics in physics
such as twistors, quantum foam, and entanglement are discussed as examples
of higherdimensional projections. The book concludes with a discussion of
the visualization of fourdimensional figures from Noll's early efforts in
the 1960's, to the work of Tom Banchoff, George Francis, and several others.
I understand that the Notices will review the book soon. Check it out.
Tony Robbin TonyRobbin []
423 Broome Street NYC, New York, 10013
tel: 212 966 6684
TonyRobbin@worldnet.att.net
http://TonyRobbin.net
http://ShadowsofReality.info
Paul
Calter:
I have two resources to list. First is a website describing the Geometry in
Art and Architecture course I designed and taught at Dartmouth. This was under
the NSF grant for Mathematics across the Curriculum.http://www.math.dartmouth.edu/~matc/math5.geometry/
The second is my
textbook, now in production, called "Squaring the Circle: Geometry in Art
and Architecture" It can be found at the publisher's website: http://www.keycollege.com/catalog/titles/squaring_the_circle.html
There is also a
link on my Dartmouth page to the Preface of the book, and a more detailed
table of contents than on the publisher's site.http://www.sover.net/~pcalter/
Maria Terrell
I have been reading the postings and I, too, have a course. About 15 years
ago I developed a course called "Geometry and the Visual World". I was developing
material for a book and have quite a bit of material written that I have usedBut
I have found the greatest success when I use original sources, and let the
students explore what they mean. It opens up the classroom to a lively discussion
as opposed to note taking.
The course as I teach it lately starts with Euclids, "Optics" (first English
translation application of elementary geometry to building an axiomatic system
from which to deduce, predict and explain common visual experiences. Optics
opens students to the idea that mathematics can be used as a tool for exploring
the difference between how things are and how they appear.
We then move to the 15th century renaissance discovery or "rediscovery" of
linear perspective. Readings and exercises are taken from Alberti's "On Painting".
We debate whether there is sufficient evidence to support the notion that
Euclids "Optics" thoughtfully applied, might have allowed the ancients to
develop a complete understanding of linear perspective which they applied
to their wall paintings. We also look for how Alberti's On Painting uses the
key theorems/definitions. We follow up with a complete investigation of 1,2,
and 3 point perspective by using Chris Zeeman's lovely workbook and video
"Geometry and Perspective", Royal Institutions Master class c. 1987. By working
all the exercises we prepare for a trip to our local museum to locate paintings
that exhibit strict linear perspective. Once there we compute the correct
place in the room from which to view them so they "pop into" that heightened
sense of depth/three dimensionality. The course ends with student projects
on applied geometry usually but not always to visual phenomena. They included
projects on the Ames Room, the Moon Illusion, application of optics to building
design, ancient astronomy, stereograms to name a few.
Maria Terrell
Senior Lecturer
Mathematics Department
Cornell University
Ithaca, NY 14853
Jay Kappraff:
I might as well put my two cents in. I taught a course in Mathematics of Design
for about 20 years. The material of this course: graph theory, symmetry, tilings,
systems of proportions, and polyhedra got incorporated in my book Connections
and a second book, Beyond Measure both available from World Scientific. In
1993, with the help of the National Endowment for the Arts, I prepared a workbook
of exercises that I did with my students through the years and in 1994 I created
a set of nine halfhour videotapes of Connections which have been shown on
cable TV numerous times. For anyone interested I could reproduce the workbook
or the videotapes. I have not taught this course for several years, but I
am thinking of updating it with the use of the great deal of software now
available. I list a few websites below although this list is not exhaustive.
I am pleased that there seems to be such an interest in teaching courses like
this. When I began, there was almost nothing like this being taught. I hope
to learn from the many new sources that you are all presenting.
Webpages:
webMathematica
http://www.wolfram.com/products/webmathematica/index.html
JavaView
http://www.zib.de/javaview/
LinKnot
http://math.ict.edu.yu/
Virtual Polyhedra
http://www.georgehart.com/virtualpolyhedra/vp.html
Symmetry and Ornament
http://www.emis.de/monographs/jablan/
Nexus Network Journal
http://www.nexusjournal.com/
KnotPlot
http://www.pims.math.ca/knotplot/