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#8501 2013-02-25 00:17:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,670

Re: Linear Interpolation FP1 Formula

repeat step 2.

Last edited by bobbym (2013-02-25 00:18:28)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#8502 2013-02-25 00:19:07

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Doing it by hand, I mean.

#8503 2013-02-25 00:26:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,670

Re: Linear Interpolation FP1 Formula

Hi;

I do not know of a hand method. I think I remember one though but do not remember where I saw it.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#8504 2013-02-25 00:26:51

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Do you remember what it was?

#8505 2013-02-25 00:27:10

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Also, why does this method solve Pell equations?

#8506 2013-02-25 00:29:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,670

Re: Linear Interpolation FP1 Formula

For that we would have to ask Mr. Fermat and Mr. Legendre.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#8507 2013-02-25 00:31:09

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

For which question?

#8508 2013-02-25 00:37:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,670

Re: Linear Interpolation FP1 Formula

How taking the cf and convergents solves a Fermat-Pell equation.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#8509 2013-02-25 00:38:28

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

It's an unsolved problem?

#8510 2013-02-25 00:46:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,670

Re: Linear Interpolation FP1 Formula

I do not think so. This is all covered in number theory books that do a little computation.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#8511 2013-02-25 04:42:42

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I will see if I can find out about it somewhere, then...

Nothing from adriana yet, 16:41. Usually on Mondays she contacts me while she is at school.

#8512 2013-02-25 04:57:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,670

Re: Linear Interpolation FP1 Formula

The method I showed is very important because it finds a simple continued fraction. This simple continued fraction's convergents are the best rational approximations of the constant. Other cf's do not have that property.

Look here:

http://en.wikipedia.org/wiki/Continued_fraction

Last edited by bobbym (2013-02-25 05:01:36)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#8513 2013-02-25 05:12:48

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I have skimmed that page for days but I've still not been able to find a method for finding a simple continued fraction that differs from yours (I believe they use your method to find the continued fraction for pi). However, I did notice that on the Wiki page for sqrt(3), they said this:

The square root of 3 can be expressed by generalised continued fractions such as [2; -4, -4, -4, ...] which is identical to [1; 1, 2, 1, 2, 1, 2, ...] evaluated at every second term.

The trouble is, I don't understand what they mean by that... this seems to be the important bit because they can get the simple CF from a generalised one. Do you know what they mean by 'evaluated at every second term'?

#8514 2013-02-25 05:19:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,670

Re: Linear Interpolation FP1 Formula

I think that is a misprint.

Generalized ones a generated using other methods some of them tricky, than the floor method.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#8515 2013-02-25 05:21:07

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

But, are the two continued fractions I mentioned identical?

They do both converge to root 3, but I am unsure how I show that they're actually the same fraction...

#8516 2013-02-25 05:26:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,670

Re: Linear Interpolation FP1 Formula

I think that is a misprint. The convergents of the two are different.

There is no 30 / 17 in the second group of convergents.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#8517 2013-02-25 05:29:16

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Hmm... so, do you remember the other way to get the simple continued fraction? Every page I go to seems to use your method but it is difficult to do by hand...

#8518 2013-02-25 05:31:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,670

Re: Linear Interpolation FP1 Formula

First things first.

does not converge to the √3


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#8519 2013-02-25 05:35:49

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Yes it does... I evaluated it after a few terms and I got root 3 with an error of only 0.0000274 %.

#8520 2013-02-25 05:39:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,670

Re: Linear Interpolation FP1 Formula

I am getting convergence to something close to 1.76393202250021


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#8521 2013-02-25 05:44:59

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

And, you are using the CF

?

I am getting root 3...

#8522 2013-02-25 05:53:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,670

Re: Linear Interpolation FP1 Formula

Yes that cf is correct but is that

{2,-4,-4,-4,-4,-4...}?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#8523 2013-02-25 05:54:38

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Yes, they are just distributing the negative through the denominator, I think.

#8524 2013-02-25 05:58:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,670

Re: Linear Interpolation FP1 Formula

I do not think that is correct.

{2,-4,-4,-4,-4,-4...} is

which is not converging to the √3

Last edited by bobbym (2013-02-25 05:59:28)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#8525 2013-02-25 06:05:44

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Hmm, I agree, that one does not converge...

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