Symmetric Linear Constructions in Motion

Douglas G. Burkholder
Renaissance Banff: Mathematics, Music, Art, Culture (2005)
Pages 403–410


In this paper we show how to create sculptures which provide a sense of motion as arbitrary irregular polygons morph into planar stellar and planar convex affine regular polygons. For example, in Figure A, an irregular pentagon is transformed into a planar stellar pentagon which is morphed into a planar convex pentagon. With the exception of a few degenerate cases, affine regular polygons appear regular when viewed from a certain direction. Although a brass sculpture would be static, the morphing of one polygon into one or more other polygons provides the illusion of motion. We give precise instructions for creating such sculptures leaving only the variable of the initial irregular polygon as a complete unknown.