TITLE:
The Hidden Geometry of the Babylonian Square Root Method
AUTHORS:
Fernanda Jaiara Dellajustina, Luciano Camargo Martins
KEYWORDS:
Babylonian Square Root Method, Newton-Raphson Method, Iterated Map, Dynamical Systems
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.19,
November
6,
2014
ABSTRACT: We propose and demonstrate an original geometric argument for the ancient Babylonian square root method, which is analyzed and compared to the Newton-Raphson method. Based on simple geometry and algebraic analysis the former original iterated map is derived and reinterpreted. Time series, fixed points, stability analysis and convergence schemes are studied and compared for both methods, in the approach of discrete dynamical systems.