Pattern Syllabus Spring 1996

3-26 Tues: Introduction to course, introduction to instructors and T.A., requirements (including discussion of final project), materials list, slide presentation, questionnaire. Short slide presentation, Discussion of symmetry, computation and labeling of symmetries of various mandalas, comparison of examples, triangle exercise, composition of symmetries, multiplication tables. Indian altars, c. 600 A.D.

3-27 Wed x-hour:

3-28 Thurs: Mandala, radial symmetry, character of circle, center and direction, negative and positive space, movement, shape, value. Gray scales.

4-2 Tues: When two different mandalas have the same symmetry, conjectures about properties common to all sets of symmetries, checking conjectures, listing of commonalities, symmetry breaking.

4-3 Wed x-hour: Critiques

4-4 Thurs: Slides and discussion of color theory. Color exercises in gouache during class. Bring in print materials for next class.

4-9 Tues: Definition of group, examples. Which figures have these symmetry groups? Groups other than symmetry groups. Examples using color triangles. Groups acting on sets.

4-10 Wed x-hour: Critiques

4-11 Thurs: Symmetry operations with block prints in class. A look at quilts.

4-16 Tues: Proof of one theorem. Infinite groups. Group-hunting and wallpaper patterns, matching by symmetries.

4-17 Wed x-hour: Critiques

4-18 Thurs: Color interaction. Slides of Albers and Vasarely. Repeat a motif using a symmetry group. Exploring simultaneous contrast in color.

4-23 Tues: How many symmetry groups have we found so far for wallpaper patterns? Are these all there are? How would one prove such a thing? In class shibori exercise.

4-24 Wed x-hour: Critiques

4-25 Thurs: Shibori-Joan Morris.

4-30 Tues: Short history of algebra.

5-1 Wed x-hour: Critiques

5-2 Thurs: Islamic art, periodic tesselation, color printing techniques, use of texture in printing.

5-7 Tues: Computation and labeling of symmetries for a wallpaper pattern.

5-8 Wed x-hour: Critiques

5-9 Thurs: Line groups, Lattices, border designs, William Morris.

5-14 Tues: Penrose tiles, symmetries of scale.

5-15 Wed x-hour: Critiques

5-16 Thurs: Exercise in designing Escher-like planar tesselations. Escher-circle limit prints and their math.

5-21 Tues: Modern painting

5-22 Wed x-hour: Final project

5-23 Thurs: Dick Birnie and crystalline structures. 3-D lattices.

5-28 Tues: Final project due!

About Math 5

This course is probably unlike any other you have taken at the college. It combines two very different disciplines in a new and unusual way. Both mathematics and art are time consuming endeavors, each in its own way. Synthesis of the two approaches will be difficult. EXPECT TO SPEND MORE TIME THAN USUAL ON THIS COURSE.

Attendance is required and will be taken every day. More than one unexcused absence will severely damage your grade in this course. Two thirds of your grade is based on work done or due in class and one third on a final project. Homework is due the day stated and late homework will not be recorded.

There is no final exam. The final project is due the last day of class. There will be no extensions of this deadline, as we anticipate needing a lot of time to grade projects properly. Furthermore, any work due after the last day of class conflicts with various regulations of the college.

This class satisfies the college's quantitative requirement.

This class satisfies the college's interdisciplinary requirement.

No mathematics beyond high school geometry is necessary.

The Final Project

The final project is worth about a third of your grade in the course. It will include original artwork, mathematical analysis of your own or other work, and will attempt a synthesis of the two. It will be graded on four points:
  • 1. Original work will be assessed according to content, technique, aesthetics, and innovative solutions to artistic, mathematical or other problems.
  • 2. Mathematical analysis will be in written form and will be graded on sophistication of analysis, clarity of presentation, and the extent to which the mathematics in the project both utilizes and supersedes what is done in class.
  • 3. Woven in with math and art there will also be a mysterious third component to your final project. Some ideas for this component would include cultural, biological, psychological, philosophical or technical aspects of math, art, design.
  • 4. Projects will be judged as to how well these three aspects are integrated.


5-2 Project proposal and literature search due.

5-16 Revised proposal due.

5-22 Preview artwork for final project.

5-28 Final project due. Expect to make a short presentation.

Readings in Math

Davis and Hersch: "The Classification of Finite Simple Groups." The Mathematical Experience.

ART Class, MATH 5 Pattern:

Wilder l04
T -TH 2:00-3:50, x period W. 4:15-5:05

Pippa Drew

Office: 206 Bradley
W: 3:00 - 4:00, Tues: 4:00-5:00

The art component of this class will acquaint you with formal design elements and several approaches to the construction of two dimensional patterns. Using gouache paint, block printing methods and, of course, your own personal intuition you avid organize design elements with symmetry operations to build effective patterns. Class will be structured around particular problems, and homework assignments will be based on concepts discussed in class. Specifically, projects will focus on ways of repeating shapes, and integrating color, value and texture effectively into these patterns. The two most important goals are to recognize the form and potential of your own work through the exploration of pattern, and to use the interplav between math and art as a footing for further interdisciplinary investigation.

Critiques and Portfolio Review are requirements

Every two weeks there will be an opportunity in the x hour to review your work with others. x hours still be in 104 Wilder. Individual final portfolio reviews will be scheduled at the end of term.

Grades will be based on

  • completion of class projects, homework on time
  • final portfolio review
  • integration of previous work into assignments
  • overall improvement and growth
  • quality of technique
  • there are no set rules in evaluating a work of art, but the following criteria occur individually, together or in various proportions:
    aesthetic quality

A few points:

  • This is not a textile design class, but the material here provides an excellent foundation for that field.
  • You do not need to draw realistically to do the artwork in this class.
  • Keep in mind that creating a tangible work of art is quite different from academic work, and the amount of time and energy spent varies from person to person depending on personal styles. Schedule blocks of time (no less than two hours with cleanup) for your studio work.


The following supplies are available at BEANS. Dartmouth Bookstore and Dukes Art Store carry many items. Dukes and Beans provide student discount cards.


2 or 3 pencils, one hard pencil for tracing
black sharpie or other large water proof marker. finer black marker
foamcore (32 x40 ) or buy a paper portfolio at DB
duck tape to make foamcore portfolios (Beans carries small rolls or share)
triangle, long side, 10 inches
2 rulers. 18 inches. 6 inches, plastic okay
x-acto knife
masking tape I 1/2" or 2"
cheap tool case or canvas bag (don't pack art supplies with books)
hammer (share) Hanover Hardware only


3 good brushes #3, #4, #6 rounds
2 cheap brushes #8 wash, #4 or 5 rounds
cheap plastic palette
small covered containers. or cans for water and mixing gouache
eye dropper (for adding water to gouache. Eastman s Pharmacy only)
Gouache paint: (no other kind of paint please)
Brands: Yarka, Winsor Newton, Pelican the small size about 1/2 ounce Yarka gouache comes In a kit with 12 colors for about $12.00. There is no turquoise or magenta. but it s the best value. You can add those two colors with other brands.
You need the following colors: yellow, ultramarine, a bright true red, black, magenta or fuscia turquoise, and a large white. Winsor Newton Process White is a cheap alternative at Beans.


cutting tools
brayer (ink roller)
safety-kut blocks for printing and stamping
Speed ball printing inks red, blue, yellow, white, black, magenta. turquoise
small square of plexiglas
free mat board scraps from Beans for mixing printing ink
rags or paper towels


graph paper 8 1/2 x 11, 6 sq. /in Quadrille
tracing paper 8 1/2 x 11 pad
sheet of black construction paper or canson paper for first assignment
An l8 by 24 pad of good drawing paper that can withstand gouache paint. It should be smoother than water color paper.
Sheets of light weight Rives paper as needed for final prints
(The retail person at Dukes or Beans can help you select paper) 60 to 90 lbs


cheap colored markers or pencils for color sketches
sponge for textured printing
drawing boards approx. 24 x 24, $8.35 DB
mat knife
portable pencil sharpener
transfer paper single sheets 9 x12, $.30; 12 x18, $.50
portfolios $3.00-6.00

Readings in Art

Martinez, Benjamin and Block, Jaqueline. Visual Forces: an introduction to design 1988. 184-229.

Ocvirk, Otto G. Art Fundamentals: theory and practice, 1981. Chapters 1, 2.

Sousmarez, Maurice. Basic Design. The Dynamics of Visual Form, 1990. Chapter 4.

On reserve:

Schlain, Leonard. Art and Physics: parallel visions in space. time and light, 1990.

Stevens, Peter S. Handbook of Regular Patterns: an introduction to symmetry in two dimensions, 1980.

Wong, Wucius. Principles of Color Design, 1987.

© Copyright 1996, Pippa Drew and Dorothy Wallace, Dartmouth College