While Statement II

Heron.java

root = 1.0; lroot = x; while (Math.abs(root - lroot) > epsilon) { lroot = root; root = (root + x / root) / 2.0; }

Heron (ca. 10-75 AD) described in his Metrica following method to compute the square root of a real-valued x:

1. Initialization: x₁ = 1

2. Iteration:
x_n+1 =
x_n +
x
x_n

2

3. Repeat step 2 until | x_n+1 - x_n | < epsilon where epsilon is the desired precision.