6.3: Babylonian and Neo-Babylonian

How Bad Was the Babylonian Exile?

This exercise is based on an ancient Babylonian method for approximating the square root of a positive number c. Assume that c lies in the interval (1,4) for simplicity. Set x0=3 / 2 . For n ≥0, define xn 1=(1)/(2)(xn (c)/(xn)) a. Use the definition of xn 1 to obtain the identity |xn 1-√(c)|=(xn-√(c))^2 / 2 xn b. Use part (a) to deduce that if xn approximates √(c) to k decimal places, then xn 1 approximates √(c) to 2 k decimal places. c. Use this algorithm to compute √(3.75) to 8 decimal places.

Python Math: Computing square roots using the Babylonian method - w3resource

Why the 4,000-Year-Old Babylonian Math Base 60 System Is Still Used

Babylonian mathematics - SlideServe