Babylonian Resistor Networks.

摘要

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 sq root of 2 to better than 0.2%, as could be done in an introductory physics laboratory.