Margaret Kepner
I enjoy exploring the possibilities for conveying ideas in new ways, primarily visually. I have a background in mathematics, which provides me with a never-ending supply of subject matter. My lifelong interest in art gives me a vocabulary and references to utilize in my work. I particularly like to combine ideas from seemingly different areas. My creative process involves moving back and forth between a math concept that intrigues me and the creation of images that interpret that concept in interesting ways using colors, shapes, and patterns. Recently, I have been employing diagrams of geometric dissections in my work, incorporating references to traditional quilt formats and games.
This piece contains 24 ‘dominoes’ and one square, arranged in a spiral pattern. Each domino has two shapes: a white square and a black polygram (or star). These shapes are cut into subparts so as to be geometric dissections of each other. For example, the upper-right domino displays a dissection of a square into seven pieces that can be reassembled into the adjacent decagon. The domino directly below also displays a dissection of a square into a polygram with 10 vertices, but with every second one connected ({10/2}). Continuing down the right-hand side, there are dominoes showing dissections of the {10/3} and {10/4} shapes. This work provides opportunities for studying the properties -- and enjoying the beauty -- of geometric dissections.
A geometric dissection is a subdivision of a shape into pieces that can be reassembled to create a different shape. In this work, a square is dissected in various ways to produce 16 different stars. These figures are all equal in area, but the dissections range in complexity from the six-pointed star at the bottom, with only 5 pieces, to the nine-pointed star at the upper-right made up of 19 pieces. The background setting for the figures is ambiguous. Are these celestial objects glimpsed through attic windows, ornaments laid away in a storage box, or, perhaps, delicate origami pieces displayed on shelves? The figures shaded in pale yellow represent true geometric stars (polygrams), while the other ones correspond to compound polygons.