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.