## Square roots (Part VI)

February 20, 2018

I’ve discussed algorithms for computing square roots a couple of times already, and then some. While sorting notes, I’ve came across something interesting: Archytas’ method for computing square roots.

Archytas’ method is basically the old Babylonian method, where you first set

$a=1$,

$b=n$,

and iterate

$\displaystyle a'=\frac{a+b}{2}$,

$\displaystyle b'=\frac{n}{a'}=\frac{2n}{a+b}$,

until desired precision is achieved (or the scribe is exhausted).

## OB Sqrt

December 22, 2015

I have discussed the problem of efficient square root calculation quite a few times. And yet, while reading Rudman’s The Babylonian Theorem, I found yet another square root algorithm. The Old Babylonian square root algorithm. Let’s have a look on how it works.