Mathematical Roots

Written by:dimport
Published by:Nightscript
Published on:2003-06-21 07:19:46

do you ever wonder how a computer calculates a square root?it's pretty simple, you just need to know how to multiply, divide, and subtract.

the method i will show you is the Newton-Raphson mthod for aproximation. it's calculus but it can be simplified for dummies.

I'll begin with the floating number 3.15

Let's turn it into a polinomial equation equaling 0;

0=(x*x) - 3.15;

I hope that you understood everything by now because it's a little more complicated than that.

There is a mathematical term called the derivative //it's ok if you don't know what it means.

the derivative of x^2-3.15 is 2x

Lets take the function in the beginning and divide it by its derivative


Now we'll make an approximation called y=1 //it cannot be equal to 0 because you can't divide by 0. For this step you will need to subtract our function from that approximation (in variable form) and replace the y by an x.

x1 = x0 - (((x0*x0)-3.15)/(2x0)) //the numbers next to the xs are subscipts
x2 = x1 - (((x1*x1)-3.15)/(2x1))
x3 = x2 - (((x2*x2)-3.15)/(2x2))
x4 = x3 - (((x3*x3)-3.15)/(2x3))
x5 = x4 - (((x4*x4)-3.15)/(2x4))
x6 = x5 - (((x5*x5)-3.15)/(2x5))
x7 = x6 - (((x6*x6)-3.15)/(2x6))
x8 = x7 - (((x7*x7)-3.15)/(2x7))
x9 = x8 - (((x8*x8)-3.15)/(2x8))

having more than 10 iterations is just excessive so we'll stop.
here is how it looks in evaluated form:


You see how the value 1.774823935 is being repeated, that means that 1.774823935 is the answer


This article was originally written by caesar4

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