Sticking to the Method
by in Feature Articles on 2008-09-30 Long before the √-button on calculators, and the now-antique slide rules and logarithm tables, people actually had to calculate square roots by hand. Like so many other pre-Computer Age tasks, square root calculation isn’t really complicated, it’s just tedious. The simplest – and, as it happens, the oldest – technique for this the Babylonian method: guess the square root of a number and then continually refine the result by taking the arithmetic mean of the result and the quotient of the number and the result, until you’re satisfied with the precision. In other words:
<script type="text/JavaScript"> var numbr = 5, guess = 2; do { guess = 0.5 * (guess + numbr/guess); } while (confirm('Refine Further? ' + guess)); </script>