Cube root can be done with a compass-and-straightedge construction. Newton's method is an iterative method that can be used to calculate the cube root. For real floating-point numbers this method reduces to the following iterative algorithm to produce successively better approximations of the cube root of "a": The method is simply averaging three factors chosen such that at each iteration. Halley's method improves upon this with an algorithm that converges more quickly with each step, albeit consuming more multiplication operations: With either method a poor initial approximation of "x" can give very poor algorithm performance, and coming up with a good initial
Square root of 5 of a side located on one the faces containing that vertex and opposite to it, are in the ratio This follows from the geometrical relationships between a cube and the quantities (edge-to-face-diagonal ratio, or distance between opposite edges), (edge-to-cube-diagonal ratio) and (the relationship just mentioned above). A rectangle with side proportions 1: is called a "root-five rectangle" and is part of the series of root rectangles, a subset of dynamic rectangles, which are based on and successively constructed using the diagonal of the previous root rectangle, starting from a square. A root-5 rectangle is particularly notable in that it can