# Priscilla Newberger

I became fascinated by mathematics and by fabric in junior high school. The interest in mathematics seemed natural. The interest in fabric started when the state of Florida forced me to take Home Economics despite my best efforts to escape. I have to admit (grudgingly) that I am glad that they did. It opened the door to the assortment of fabric and fiber that can be completely utilitarian or amazingly beautiful and expressive. I have chosen to use the techniques of patchwork and appliqué to illustrate mathematical tiling and the methods used to generate the tiling. I hope to make the beauty of this sophisticated mathematics readily accessible.

I have created a part of a non-repeating Penrose-like tiling consisting of rhombi with acute angles of π/7, 2π/7 or 3π/7. The tiling was hand pieced in silk using the English paper piecing technique.The color placement is not mathematically significant, but was chosen to highlight areas of symmetry. This patchwork is appliqued onto a hand quilted and embellished cotton background. The quilting lines are the elegant grid consisting of seven sets of parallel lines described by DeBruijn that comprise one method of generating this tiling. The lines are offset so that at most two can intersect at any point.The angles of intersection determine the choice and orientation of the next rhombus in the tiling. Mathematical tilings are a natural for patchwork and other fiber techniques. The acute angles present a challenge, as does working with silk, but the luster and beauty of the silk make it worthwhile.