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Oh. That's actually very helpful. I hadn't realised Newton--Raphson could be that easy to use in practice. The closeness between 1.47 and 144 did strike me.
by kqr 1y ago
Oh. That's actually very helpful. I hadn't realised Newton--Raphson could be that easy to use in practice. The closeness between 1.47 and 144 did strike me.
- FabHK 1y agoIndeed - taking the square root of numbers iteratively is very satisfying, because of the super fast convergence. Sqrt 10: Guess 3, then residual is 10 - 33 = 1, so next guess add 1/(23) = 1/6, so now we're at 3.166..., and the square of that is 10.0277..., so you're very close already.
- jacquesm 1y agoI did this in high school when we weren't allowed a calculator during tests and got into an argument with a teacher who told me that it is impossible to do this in your head so I must have cheated. A short demonstration on random numbers sufficed. I've taught my kids the method and they are now set up for similar arguments ;) The hardest part if you want to generate more digits is to keep track of the intermediary sum during the multiplication, that's why I never got past three significant digits. That would be an interesting little contest though!