Babylonian method for calculating the square root
Ancient Babylon, about 1600 years before Christ walked, have developed a complete turn of mathematics which continues to interest many researchers in the history of mathematics.
In this article we will review briefly the Babylonian method for calculating square root, which provided very accurate and impressive results considering the absence of any numerical technology in this period.
lets Begin demonstrate the method through an example:
Suppose for example that we try to find out the square root of the number 18
The starting point is through expression of the number 18 as the sum -or difference- of two values that one of them is the nearest whole root, in this case we write:
16 +2 = 18
the Number 16 is the square root of 4, therefore the square root of 18 is 4 added to the difference (2) divided by the whole root is two times (2 times 4 that means to 8)
Explanation:
The root of the number 16 is 4
The difference between 18 and 16 is 2
The whole roof multiplicated in 2 is 4*2=8
The square root of 18 = 4 + (2 / 8 ) = 2.25
By this method we get the root of 18 is 4.25, while the calculator result is 4.24264 so that the difference is 0.00736 which considered very high accuracy.
Now I will explain the general method:
We want to calculate √a When a = b2 ± c
Notice that the root of b^{2} is b
The difference between √a and b^{2} is c
Using the algorithm described we get that
The square root of a is b + ( c / 2b ), the end dont forget to rate the article