Can anyone help me with a square root algorithm that I made up?
Your algorithm is an iterative method. Iterative methods belong to the Numerical Analysis field, and although they have been around for ages, numerical methods were considered to have too many calculations in them to be viable when done by hand, even with the use of a scientific calculator, because human error can creep in. When computers came along Numerical Analysis took off big time. You could implement your numerical method into the computer, and the computer would do all the iterations and number crunching that was necessary with minimum error. I know you say that you want to execute your algorithm without a calculator, but to be honest, without using a computer your algorithm is going to be prone to error, because of all the hand calculations necessary, especially if you manage to get it working for numbers in their thousands, tens of thousands etc… I’m not trying to knock your algorithm, just advising you that if you get it working, it may be worth writing a little loop using
