Babylonian resistor networks

The ancient Babylonians had an iterative technique for numerically approximating the values of square roots. Their method can be physically implemented using series and parallel resistor networks. A recursive formula for the equivalent resistance Req is developed and converted into a nonrecursive solution for circuits using geometrically increasing numbers of identical resistors. As an example, 24 resistors R are assembled into a second-order network and Req/R is measured to equal √ 2 to better than 0.2%, as could be done in an introductory physics laboratory. (Some figures may appear in colour only in the online journal)