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 SIGMAA-ARTS. The responses are listed; some include links to websites, names of books and the e-mail 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 intro-to-drawing 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 one-semester 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 Viewpoints-9-18-06.pdf You might also be interested in the file called Discussion-Problem4.pdf This file discusses "Problem 4 of Lesson 4" which has now become problems 5--9 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 17604-3003
phone number: 717-291-4222

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/math-art-arch.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 math-art 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 face-to-face classes as well. Perhaps my most interesting self-made 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 four-dimensional 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 higher-dimensional projections. The book concludes with a discussion of the visualization of four-dimensional 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 used--But 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 half-hour 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.
Web-pages:
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/virtual-polyhedra/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/

webmaster   Editor