Third root

the current estimate (est) is cubed and checked to see if the absolute value of that cube and the number whose cube root is being sought have a difference greater than accuracy. if yes, the while-loop continues to execute.

btw, if anyone is going to use this there are better ways to create a first estimate than starting with num/6.

kglad, I've had a look at Newton's method and the function cubeRootF(), tried to figure it out but failed. Could you explain one thing: how is accuracy used in the function?

you're welcome. and yes, luigiL, that's correct. (and yes, that is not a recursive formula. it's more properly called an iterative process.)

Thank you very much, kglad.

>> function cubeRootF(num, accuracy) {
est = num/6;
while (Math.abs(num-est*est*est)>accuracy) {
est = (est*2+num/(est*est))/3;
}
return est;
}

Good formula - but it's not recursive.

--
Dave -
Adobe Community Expert
www.blurredistinction.com
www.macromedia.com/support/forums/team_macromedia/

yes, i don't think flash version 1 dates back too many centuries.

the cube root recursive formula above is a special case of newton's method and in its earliest version may have been used by the babylonians thousands of years ago to calculate square roots using:

est =(est + num/est)/2.

in general, the nth root can be calculated by extending the babylonian algorithm using:

est=(est*(n-1)+num/Math.pow(est,n-1))/n

But the cube root of x is simply x^(1/3). This holds in all cases -- the yth root of x = x^(1/y).

Can't you just use that? In this form, it's exact.

But the cube root of x is simply x^(1/3). This holds in all cases -- the yth root of x = x^(1/y).

Can't you just use that? In this form, it's exact.

So cool to see how to calculate cube roots. Thanks kglad. I'm not sure that specific "code" has been known for hundreds of years, but I suspect the algorithm is. Just have to tease you a little bit since I envy your math kung-fu!

there are many ways to calculate cube roots. in general, for calculating nth roots (including 3rd roots), jeckylls suggestion is the easiest to employ.

for cube roots, using a simple recursive formula is faster and may be helpful if you're calculating many 3rd roots. the code below is probably the best known (for hundreds of years):