07-13-2026, 03:59 PM
Square Roots in the Babylonian Way
Summary
The article explores the ancient Babylonian method for calculating square roots and explains why this simple technique is still mathematically impressive today. The method begins with an initial guess and repeatedly improves it by averaging the guess with the number divided by that guess. Although developed thousands of years ago, this process is closely related to the modern Newton–Raphson method, which is used in numerical calculations. The author shows, using only basic algebra, that the method always moves closer to the true square root regardless of the starting point.
Each new approximation reduces the error, and eventually the accuracy improves extremely quickly through a process called quadratic convergence. This means that the number of correct digits can roughly double after each step. Through examples such as finding √2 and √22, the article demonstrates how a simple ancient idea can achieve remarkable precision. Ultimately, it highlights the elegance of Babylonian mathematics and shows that powerful mathematical ideas do not always require advanced theories to be understood.
ARTICLE
Summary
The article explores the ancient Babylonian method for calculating square roots and explains why this simple technique is still mathematically impressive today. The method begins with an initial guess and repeatedly improves it by averaging the guess with the number divided by that guess. Although developed thousands of years ago, this process is closely related to the modern Newton–Raphson method, which is used in numerical calculations. The author shows, using only basic algebra, that the method always moves closer to the true square root regardless of the starting point.
Each new approximation reduces the error, and eventually the accuracy improves extremely quickly through a process called quadratic convergence. This means that the number of correct digits can roughly double after each step. Through examples such as finding √2 and √22, the article demonstrates how a simple ancient idea can achieve remarkable precision. Ultimately, it highlights the elegance of Babylonian mathematics and shows that powerful mathematical ideas do not always require advanced theories to be understood.
ARTICLE
┌────────────────────────────────┐
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘