Babylonian Resistor Networks

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2012
Accession Number
ADA560037

Entities

People

  • Carl E. Mungan
  • Trevor C. Lipscombe

Organizations

  • United States Naval Academy

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Differential Equations
  • Electronic Mail
  • Equations
  • Gravitational Fields
  • Information Operations
  • Irrational Numbers
  • Kinetic Energy
  • Mathematics
  • Measurement
  • Numbers
  • Physics
  • Physics Laboratories
  • Resistance
  • Resistors
  • Square Roots
  • United States Naval Academy

Readers

  • Approximation Theory.
  • Electrical Engineering