Exploring the Babylonian Method and Trigonometric Approach for Square Root Calculation a Python-Based Analysis

Abstract

This paper explores various applications for solving square root values using the Babylonian method. By thoroughly analyzing this ancient method, we have derived a formula for calculating square roots, which is demonstrated and verified through Python programming. This formula allows for the computation of square roots for any number, both rational and irrational. While the exact square root cannot always be expressed through a simple formula, this study draws connections between the Babylonian method and trigonometric functions to create an effective approach for square root approximation. We demonstrate the practicality of this approach through Python, providing a computational tool based on this historical technique.