Babylonian Method

More than 3000 years ago, the Babylonians invented a simple and incredibly accurate method for calculating square roots. This video explains how it works.

[LosizakII]

That was a really good way of explaining it. Thank you.

[jacolansac]

Out of curiosity... What method is the calculator using?

[毛氈苔]

Thank you very much for explanation. I had programmed it before but don't know why. Now I understand it more correctly

[brettknoss]

I was looking into the Babylonian Method, after watching prof Alan Edleman show how to do Automatic Differentiation in Julia.

[dennissanchez]

Your explanation was excellent, thanks.

[robertmaxwell]

Do you have to guess below the precise square root first? like for 3 I guess 1.1 instead of something like 1.6...

[WyrdieBeardie]

Another great thing about this algorithm is that it can be rewritten as:
X - ( (X/2) - (a/2X))
So what is good about this? Well, if you are only interested in the integer portions, the division by 2, and the multiplication by two can be converted to very fast bit shifts leaving only 1 integer division per iteration.
For 16-bit numbers, it only needs an average 1 to 3 iterations, the average being less than 2. And this integer approximation for numbers 1- 65536, is only off by 1 in 127 cases! Not too shabby for a 3000 year old algorithm 😃

[aastham]

Excellent explanation. Thank you very much.

[dakshnarang]

Thanks for this video. Very well explained THANK YOU!!!

[WyrdieBeardie]

Thank you for the excellent explanation. One question I do have is how does this differ from "Newton's Method" with respect to finding square roots?

[basemnouh]

Could you plz send us the Matlab code ?

[marlopez]

I have to say to you that x times a/x is a but notice that x can not be 0 because 0 times infinity is an indetermation, ax/x is a for all real numbers x-{0}