On the Shape of a Violin
Roel J. Stroeker · Mathematics Magazine · 2015
SummaryFor centuries luthiers—that is, instrument makers of violins and other stringed instruments—had no more sophisticated tools at their disposal to define the shape of their instruments than marked ruler and compass. Today, modern aids are available in terms of computational power and expertise in graphic design to assist them in this respect. This raises the following question: How can these powerful computational techniques be applied in the process of searching for a form of the violin both pleasing to the eye and optimal in some mathematical sense? In this paper, I use parametric cubic splines in an attempt to come close to and possibly improve upon—strictly in a mathematical and visual sense—the shape of a violin as laid down by the great masters of the past. The main reasons for choosing the cubic spline are: good approximation properties, simplicity of construction, and most importantly, its unique curvature properties.