Download Math 8: SYMMETRY Professor M. Guterman Throughout history

Math 8: SYMMETRY
Professor M. Guterman
Throughout history people have used symmetric designs to
decorate their surroundings. In this course we will discuss the
symmetries of wallpaper patters such as the student-drawn
example to the left. Our approach illustrates the powerful theme
in modern mathematics: we associate to each pattern a
mathematical object called a group (consisting of the symmetries
of the pattern) and we use these groups to classify the patterns.
Our main mathematical goal will be to show that there are only
17 types of wallpaper patterns. As we proceed with the
mathematical discussion, we will learn to identify the symmetries
of given patterns, with a special emphasis on the periodic
drawings of M. C. Escher. In addition, we will learn to draw
such patterns ourselves.
The mathematical prerequisite for the course is high school
geometry (including some exposure to the congruence of
triangles and the rudiments of analytic geometry: Cartesian
coordinates, the distance formula, etc.). The course counts
toward the Mathematical Sciences distribution requirement, but
does not count towards a concentration in Mathematics.
Texts:
Doris Schattschneider: Visions of Symmetry- Notebooks,
Periodic Drawings, and Related Work of M. C. Escher, W. H.
Freeman and Co., New York, 1990.
Martin M. Guterman: Symmetry Groups of the Plane, notes
available through the Math Department.