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
Rubik's Cube followed by another 3×2×1 on the opposite side. Next, the corners of the top layer are solved. The cube can then be solved using only moves of the U layer and M slice. Most beginner solution methods involve solving the cube one layer at a time, using algorithms that preserve what has already been solved. The easiest layer by layer methods require only 3–8 algorithms. In 1981, thirteen-year-old Patrick Bossert developed a solution for solving the cube, along with a graphical notation, designed to be easily understood by novices. It was subsequently published as "You Can Do The Cube" and