The Simplest Cubic Root

The architectural symmetry of Cubic polynomials supports many root approximation methods, helping intuitive understanding and with a little work, can be transposed to higher orders to minimise more complex math. This post expands on an earlier post, Cubic Polynomials — Using Similar Triangles to Approximate Roots, which promoted the use of Similar Triangles derived from Turning and Inflection Points.

Both methods are very simple and it is difficult to quantify pros and cons in a short post. The latter, being very easily formularised and not requiring calculus beyond finding the Inflection Point Ip is the quicker and simpler of the 2, is best suited when Ip(x)=B/3A