Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: Root
Replies: 21   Last Post: Jul 14, 1999 3:46 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
carel

Posts: 161
Registered: 12/12/04
Re: Root
Posted: Jul 11, 1999 9:42 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply



The method of Newton is very elegant to solve for roots

Let f(x) = x^2 - A where A is the number to get the square root from.

Then g(x) = f'(x) = 2x

Then xnew = xold - f(xold)/g(xold) = xold - [xold^2 - A]/[2xold]

So guess a value for x and then obtain a new guess value.

You will soon obtain x = A^(.5)

In general you can obtain any root by letting f(x) = x^n - A and g(x) =
nx^(n-1)

Carel
James Adelman wrote in message <378894F7.MD-1.2.j.adelman@ukonline.co.uk>...
>James Adelman wrote on 11 Jul 99 12:57:39 +0000 in sci.math:
>

>> Kaimbridge wrote on Sun, 11 Jul 1999 08:52:29 GMT in sci.math:
>>

>> > In article <k4Ph3.7360$Le1.136634@news2.randori.com>,
>> > "User" <pohanl@aol.com> wrote:

>> > >
>> > > Does anyone know how to go about doing a square root or cube root
>> > > calculation?

>> >
>> > There was a good post on "the hand method" done back in January:
>> >
>> > http://www.deja.com/=dnc/getdoc.xp?AN=433077696
>> >
>> > ~Kaimbridge~
>> >

>> An alternative might be to use the binomial expansion, although this
>> will probably make for a lot more arithmetic than the one at the
>> URL above; it _may_ need fewer terms for accuracy, but I don't think
>> so, you's have to try it.
>>
>> Let's try 57:
>>
>> 57^.5=49^.5*(57/49)^.5
>> =7*(1+8/49)
>>

>Missed some brackets: should be
>
>

=7*[(1+(1/2)(8/49)+(1/2)(-1/2){(8/49)^2}/2+(-3/2)(-1/2)(1/2){(8/49)^3}/3!+..
.]
>>
>> It works, but without a calculator (or even with one) it requries lots
>> of effort. I suppose the only good news is the factorial on the
>> bottom.
>>

>> > --
>> > Note that "news" in "@my-dejanews.com" has been
>> > dropped.
>> >
>> >
>> > Sent via Deja.com http://www.deja.com/
>> > Share what you know. Learn what you don't.

>>
>> --
>>
>> James Adelman

>
>--
>
>James Adelman









Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.