The Hidden Geometry of the Babylonian Square Root Method

• 作者: Fernanda Jaiara Dellajustina Luciano Camargo Martins
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Babylonian Square ROOT METHOD NEWTON-RAPHSON METHOD ITERATED Map DYNAMICAL Systems
• 年，卷（期）: 2014,（19）
• 页码范围: 2982-2987
• 页数: 6页
• 分类号: O1

摘要

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.