105TORUS

Behind the geometry of a doughnut, a quartic equation that has to be solved numerically.

The logical follow-up to the previous project, with a markedly trickier figure: the torus. Where a sphere leads to a quadratic equation, a torus produces a quartic one. The project sets geometry aside to concentrate on the heart of the problem: finding the root of that polynomial, and above all comparing three iterative methods that each get there at their own pace — one slow but sure, another fast but temperamental.

Numerically solving a quartic equation given by its coefficients, through bisection, Newton's method or the secant method, printing each iteration up to the requested precision.