The Birthday of Niccolò Paganini (1782) – Mathematics of Violin

Paganini was a virtuoso violinist. The mathematics of violin: the shape (arch top, f‑holes) is designed using curves (cycloids, catenaries). The frequencies of the strings follow the law of harmonics: f = (1/2L)√(T/μ). The bridge transfers vibrations to the body, which radiates sound via the Helmholtz equation (a PDE). Paganini’s caprices use rapid fingerwork – a form of algorithmic complexity. Violin making is applied geometry and wave physics. No wonder Stradivarius instruments are prized – they solve a difficult optimisation problem.