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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

I don't think. If we did, I do not remember them.

Could you post them? I do not have access to his books atm.

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,105

He goes into it fairly deeply and it is an acquired skill but more simply we can try to get an x on the left and the rest of them on the right.

The cf is already one of those but we will create others.

start with an initial guess of 3.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

That one I know.

Just for the sake of an answer, x=3.302775638...

*Last edited by anonimnystefy (2013-11-21 12:56:32)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,105

Then produce another one.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

It cannot be produced using either this or the previous iteration formula.

It is not stable at that point, but we can do -1/x_1 to get it.

*Last edited by anonimnystefy (2013-11-21 13:27:55)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,105

What one?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

Huh?

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He means which one

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,105

Which iterative form are you talking about?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

Both. sqrt(3x+1) and 3+1/x.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,105

The sqrt one is not stable? Why?

**In mathematics, you don't understand things. You just get used to them.**

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What are you two talking about?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

It is stable, but converges to the positive root only.

But, as I suggested, we can get -1/(positive root) to get the negative root.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,105

Yes, and that is a very stable numerical idea.

Do you know how to program the iteration in M?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

Should I use Nest?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,105

Yeparoo!

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

Okay, it was an easy one.

I use this method to get roots of equations on my calculator.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,105

What method?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

Iteration.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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But it is easier with M.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

True. But I cannog access M in class, whereas I can access a calculator. It has an astounding 100 digits of accuracy available.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,105

Which calculator? TI-92 has 640 digits.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

It's a Chinese Kenko. We don't have TI's over here and besides, they are too expensive. This one cost a bit more than a buck.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,105

The new rasberries look fantastic.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

I saw the blog entry. They must be expensive as hell!

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