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You are not logged in. #8501 20130225 23:17:43
Re: Linear Interpolation FP1 Formularepeat step 2. Last edited by bobbym (20130225 23:18:28) 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. #8502 20130225 23:19:07#8503 20130225 23:26:04
Re: Linear Interpolation FP1 FormulaHi; 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. #8504 20130225 23:26:51#8505 20130225 23:27:10
Re: Linear Interpolation FP1 FormulaAlso, why does this method solve Pell equations? #8506 20130225 23:29:29
Re: Linear Interpolation FP1 FormulaFor 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. #8507 20130225 23:31:09#8508 20130225 23:37:56
Re: Linear Interpolation FP1 FormulaHow taking the cf and convergents solves a FermatPell 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. #8509 20130225 23:38:28#8510 20130225 23:46:03
Re: Linear Interpolation FP1 FormulaI 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. #8511 20130226 03:42:42
Re: Linear Interpolation FP1 FormulaI will see if I can find out about it somewhere, then... #8512 20130226 03:57:38
Re: Linear Interpolation FP1 FormulaThe 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. Last edited by bobbym (20130226 04:01:36) 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. #8513 20130226 04:12:48
Re: Linear Interpolation FP1 FormulaI 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: #8514 20130226 04:19:10
Re: Linear Interpolation FP1 FormulaI think that is a misprint. 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. #8515 20130226 04:21:07
Re: Linear Interpolation FP1 FormulaBut, are the two continued fractions I mentioned identical? #8516 20130226 04:26:03
Re: Linear Interpolation FP1 FormulaI 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. #8517 20130226 04:29:16
Re: Linear Interpolation FP1 FormulaHmm... 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 20130226 04:31:51
Re: Linear Interpolation FP1 FormulaFirst 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. #8519 20130226 04:35:49
Re: Linear Interpolation FP1 FormulaYes it does... I evaluated it after a few terms and I got root 3 with an error of only 0.0000274 %. #8520 20130226 04:39:33
Re: Linear Interpolation FP1 FormulaI 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. #8521 20130226 04:44:59
Re: Linear Interpolation FP1 FormulaAnd, you are using the CF ? I am getting root 3... #8522 20130226 04:53:17
Re: Linear Interpolation FP1 FormulaYes that cf is correct but is that 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. #8523 20130226 04:54:38
Re: Linear Interpolation FP1 FormulaYes, they are just distributing the negative through the denominator, I think. #8524 20130226 04:58:51
Re: Linear Interpolation FP1 FormulaI do not think that is correct. which is not converging to the √3 Last edited by bobbym (20130226 04:59:28) 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. #8525 20130226 05:05:44
Re: Linear Interpolation FP1 FormulaHmm, I agree, that one does not converge... 