Conics from Polygons: The Chord Ratio Construction

Scott Vorthmann, David Hall and David Richter
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 269–276 Regular Papers


We present a new technique for constructing conic sections and quadric surfaces, or more specifically, points on those curves and surfaces. The technique, called the chord ratio construction, takes a single numeric parameter and three input points, producing a fourth point. We show how the parameter value determines what curve or surface is constructed when the construction is iterated. Along the way, we present some artworks that both inspired these results, and were inspired by them.