This project uses an ancient algorithm for approximating the square root of a number, a. Set the √(a) to the value of a you would like to approximate the square root of (Xn). Set the Guess slider to any number as your guess (Xn-1). Click on the green flag. What algorithm does Scratch use to compute the square root of a number? Does anyone know?
The National Math Standards K–12 do not mention the mathematical technique known as 'iteration'. Iteration is the tool used to explore fractals and chaos. I use the Sumerian square root algorithm as an introduction to iteration. The formula to be iterated appears on the project screen. Iteration begins with a single value (often called the seed) and all successive values are computed by taking the output of the function and plugging it back into the function as its next input. This process of taking the output as the next input is repeated as many times as needed. The Sumerian square root algorithm converges quickly for such a simple process. For the derivation of the formula visit www.scratch-blog.com
