Last time MAT 103 creator Margaret Groman taught the course (Spring 1999)
she was given a remarkable souvenir by her graduating student Crystal
Here is the story, in Crystal's own words:
The first pattern comes from the Iroquois border designs. It is an
one-dimensional pattern known as a p111, translation only.
pattern is an Ojibwa design used on beaded belts. It has translation and
horizontal reflection, which makes it a p1m1.
The next four designs are
all Iroquois designs used for quiltwork, bead work and applique on
garments and maccasins.
The first one is a pm11 because it has translation
and vertical reflection.
The second is a p112, which has translation and
The third border design has glide reflection with translation
which makes it a p1a1.
The fourth is a pmm2, because it has translation,
horizontal and vertical reflection with rotation.
The last pattern is an
Ojibwa design used on beaded belts. It is known as a pma2 which has all
the isometries except horizontal reflection.
I used Iroquois and Ojibwa designs because they are part of my heritage.
I am half Ojibwa and half Oneida, one of the Iroquois tribes. I've
researched the designs at the library, then drew each out individually on
tracing paper. After that I transferred the images to a silk screen and
printed out on paper. I' ve found the seven possible combinations of
isometries from my own culture, using one-dimensional patterns.
Lyford, Carrie A. Iroquois Crafts. Wisconsin: R. Schneider, 1982.
Lyford, Carrie A. Ojibwa Crafts. Kansas: Haskell Institute, 1943.
Naylor, Maria, ed. Authentic Indian Designs. New York: Dover Publications,
Farmer, David W. Groups and Symmetry. American Mathematical Society, 1996.