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Babylonian square root approximation
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How to calculate square root with Babylonian method?
This method can be derived from (but predates) Newton–Raphson method. 1 Start with an arbitrary positive start value x (the closer to the root, the better). 2 Initialize y = 1. 3. Do following until desired approximation is achieved.
What was the rate of convergence of the Babylonian method?
However, for the Babylonian method we are not talking about a rate of growth, but a rate of convergence. The sort of convergence exhibited by the Babylonian method is indeed called quadratic convergence, as you can read about here: http://en.wikipedia.org/wiki/Quadratic_convergence.
How is the Babylonian method used in math?
The first method is often called the “Babylonian method” since it was known to the ancient Babylonians. Here’s how it works. Say we are trying to find the square root of N. Just like with the guess and check method, we start out with some guess R. Then we compute a new value for R as follows:
How did the Babylonians solve the equation Y3?
Putting y = ax/b gives us the equation y3 + y2 = ca2/b3 which can be solved by looking up in the table to find the value of y and then substituting back. It is amazing that without the use of modern notation for these equations the Babylonians could recognise equations of a certain type and the methods for solving them.
Last Update: Oct 2021
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This image shows Babylonian method calculator.
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