## sarah-marie belcastro

* “Connected sum of four projective planes”*

Philosopher's Wool with rayon inclusions, 12" x 9" x 3", 2006.

”

In the classification of topological surfaces, any surface may be expressed in
a normal form of the connected sum of tori or the connected sum of projective
planes, where the genus of the surface is measured by the number of constituent
surfaces. This piece is the connected sum of four projective planes (or, equivalently,
two Klein bottles). Each rayon stripe corresponds to twice a homotopy generator
for the surface, one generator for each Klein bottle.

sarah-marie belcastro, Visiting Assistant Professor and Associate Director for
the Center for Women in Mathematics, Smith College, Co-Director Hampshire College
Summer Studies in Mathematics

"I knit topological surfaces from natural fibers. What distinguishes my
art creations from ordinary classroom models is the choice and placement
of yarns and the care in execution and attention to detail. Even simple
mathematical objects can be beautiful."
http://www.toroidalsnark.net

**Another work by the artist **
* “Connected sum of five projective planes”*

Beaverslide Dry Goods Wool, 13" x 9" x 5", 2006.

In the classification of topological surfaces, any surface may be expressed in
a normal form of the connected sum of tori or the connected sum of projective
planes, where the genus of the surface is measured by the number of constituent
surfaces. This piece is the connected sum of five projective planes. The five
constituent projective planes are knitted with five different colors of the same
wool; that is, each projective plane is a different color.