A really cool algorithm described in that manuscript is an approximation for finding the square root of a number. What I liked about this algorithm is that its handy. You could quickly approximate the square root of a real number with just some basic division and addition.
This is how the algorithm works:
- If 'X' is the number you want to find a square root of, find the nearest whole number 'N' that approximates it. So if X = 23.2 then N = 5.
- Find the difference between X and N*N. Call it D. In this case it works out to -1.8. This should be too tedious to work out either.
- Now comes the magical part, divide this difference (D) by 2*N. So that's -1.8/10. Again, this shouldn't be that difficult to do in your head, -0.18.
- The approximate value of the square root of X is simply N + D/2N = 5 - 0.18 = 4.82
The true value for an approximation of the square root of 23.2 is 4.8166, very close...
A detailed write up of the algorithm and other dating techniques used can be found here