Department of Mathematics, University of Wisconsin, Madison
I like to crochet hyperbolic surfaces. Their smooth lines and curved surfaces show a very beautiful play of light and shadow at dusk and dawn. If the crochet is with holes the surface can also be used as a lamp shade and again the play of the light is fascinating. It makes me very happy to have discovered this beautiful connection between mathematics and art.
Pink and Red Trumpet
Yarn and Shaped Line
This is a hyperbolic disk with a hole. Depending on the variations in curvature it can take many shapes. It could be around structure with a hole in the middle. Or, as in this case, if you leave out a point at infinity, you will get a long tube with close to 0 curvature. As the curvature increases ever more you get the typical wavy shapes of a hyperbolic surface along the perimeter.
White Riemann Surface as a Lamp Shade
This surface is made up of more or less flat layers with circular holes connected by tubular handles. Homotopically it is equivalent to a collection of circles attached to each other in various places. It was an attempt to make a construct similar to what Eva Hild does with her sculptures, no comparison, though! But with a light tube running through it, it has some nice shadow play.
A Seifert Surface as a Hyperbolic Lamp Shade
This surface started out as an annulus with 14 bands attached to its rim. Seven alternate bands were combined above the annulus and seven below. However before they were crocheted together respectively, each band was twisted. Finally a tube connects the top rim with the bottom rim and runs through the middle annulus. Through this tube I ran a light tube. It makes for an interesting lamp shade.