Ancient Sumer was located in southern Mesopotamia in what is now called Iraq. Sumerian history dates to 5000 BC. In 2340 BC, Sargon I founded the Akkadian dynasty. By 200 BC Sumer had declined to the point of eventually being absorbed by Babylonia

and Assyria.

The
Sumerians are believed to have invented the cuneiform system of writing on clay
tablets with a cut reed.

*iteration*.

*Iteration*is a special form of ‘looping’ where given an initial input (called the

*seed*) to a function, the output becomes the next input.

Suppose one wants to compute √(a). One picks a guess,
x

_{n-1}, plugs it and*a*into the formula to compute x_{n}. This output, x_{n}becomes the new input, x_{n-1}and a new output is computed. Do this repeatedly and x_{n}converges to the √(a).
http://scratch.mit.edu/projects/45120106/

A free PDF document explaining how thew formula is derived can be had by sending an email request to

grandadscience@gmail.com.