On a geometry of the flat violin boundary

摘要

An analytic expression for the shape of the flat boundary of the violin is suggested. The polar equation in the form (r/a)n = 1 − 2Σm = 1N − 1cmsin2(mθ/2) has been assumed for the upper and lower bouts, whereas the C-bout has been represented by a rotated and translated ellipse. The parameters and the coefficients, computed numerically to fit a 1720 Stradivarius, are tabulated in the text.