The violin arcs

摘要

Simple models for the violin arcs (the curves obtained by the sections of a curved violin surface by vertical planes along and across the length) in terms of polynomials and rational functions in rectangular coordinates have been suggested. The coefficients appearing in the corresponding equations are given as the solutions for the associated linear system generated by fitting no more than five data points. No more than five coefficients are required to generate the arcs. The graphs of these equations for the central longitudinal arcs and six lateral arcs at the conventional violin makers' position for both the top and the back plates have been given. The combined set of equations represent the surface of a curved violin plate and can be used to produce three dimensional graphs of various violin models (which however have not been presented in this article).