3 ms·
The babylonian method is, imo, easier to remember and perform than the "lost art" presented here: Start with a ball park estimate of the root of x, then take a
by ballenf 9y ago
The babylonian method is, imo, easier to remember and perform than the "lost art" presented here:
Start with a ball park estimate of the root of x, then take an average of (estimate + x / the estimate). That's your new estimate. Rinse and repeat until convergence to an acceptable degree.
The biggest drawback if doing this by hand is the division problem can be a pain.
I see the attraction and "purity" of the proposed lost art.
- Houshalter 9y agoDivision is much harder than multiplication. Even for computers. It's easier to just square your estimate and see how close it is. Then increase or decrease it proportional to how much closer you are getting.
- nicolapede 9y agoFascinating, I didn't know the babylonian method -- it sounds equivalent to Newton's.
- mark-r 9y agoI had always thought of this as Newton's Method too, but that's because I was simply misremembering the fullness of Newton's Method [1]. I'm grateful for the education. https://en.wikipedia.org/wiki/Newton%27s_method https://en.wikipedia.org/wiki/Newton%27s_method
- jostylr 9y agoIt is equivalent when applied to the function f(a) = a^(1/2) - x. Also, one needs to divide by 2 since if a is the square root of x, then a+x/a = a + a = 2a. n-th roots are not quite as nice, but still work fairly simply: ((n-1) a + x/a^(n-1) )/n You can see that the fixed point (a = nth root of x) works out as it should.