Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #8526 20130226 05:09:11
Re: Linear Interpolation FP1 FormulaYes, the general form for a simple cf is 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. #8527 20130226 05:16:13#8528 20130226 05:22:30
Re: Linear Interpolation FP1 FormulaThey are not the same obviously but we might be able to prove they both converge to the same thing. 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. #8529 20130226 05:26:53
Re: Linear Interpolation FP1 FormulaThey said something about evaluating that first fraction at every second term, to get the second fraction... #8530 20130226 05:28:22
Re: Linear Interpolation FP1 FormulaAnd how does that prove they are the same? 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. #8531 20130226 05:30:13
Re: Linear Interpolation FP1 FormulaIt doesn't but they are claiming there is a way to get the simple CF from the first one... #8532 20130226 05:42:38
Re: Linear Interpolation FP1 FormulaI do not see any way right now of deriving one from the other. 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. #8533 20130226 06:17:11
Re: Linear Interpolation FP1 FormulaWhat methods of proof do you use? #8534 20130226 06:18:57
Re: Linear Interpolation FP1 FormulaConsider her dead meat. 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. #8535 20130226 06:23:27
Re: Linear Interpolation FP1 FormulaYou may be right... this could venture into F territory. Something is wrong. Just a pity it ended so abruptly. #8536 20130226 06:26:51
Re: Linear Interpolation FP1 FormulaNo; Last edited by bobbym (20130226 06:27:21) 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. #8537 20130226 08:56:03
Re: Linear Interpolation FP1 FormulaSorry, I had to take my sister to my grandmother's house. #8538 20130226 09:08:28
Re: Linear Interpolation FP1 FormulaHi; when you solve for x you get √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. #8539 20130226 09:10:47
Re: Linear Interpolation FP1 FormulaYes, that is what I meant  eventually when you follow those steps, you get the original fraction (x again). #8540 20130226 09:11:58
Re: Linear Interpolation FP1 FormulaYes, somewhere in th cf there will be a repeat of x. You just replace it and solve for x. 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. #8541 20130226 09:15:26
Re: Linear Interpolation FP1 FormulaThat seems pretty handy to check if these Wikipedia CFs converge as they're supposed to... but, I suppose this method might be hairy if you have a long period, for large n, say. #8542 20130226 09:16:40
Re: Linear Interpolation FP1 FormulaIt is easier to use numerical methods and arrive at an experimental result. 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. #8543 20130226 09:26:06
Re: Linear Interpolation FP1 FormulaWe looked at continued fractions and applying them to solve Pell's equation, are there any applications of infinite nested square roots? Those seem interesting too. #8544 20130226 09:36:55
Re: Linear Interpolation FP1 FormulaI do not know of any offhand apps but they are solved in the same way as a cf. 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. #8545 20130226 09:42:48
Re: Linear Interpolation FP1 FormulaYes, I have read about them. The Wiki article is a lot shorter than the CFs one though. #8546 20130226 09:46:35
Re: Linear Interpolation FP1 FormulaThey are less useful apparently. CF's are very big in number theory and numerical analysis. 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. #8547 20130226 09:48:28
Re: Linear Interpolation FP1 FormulaWhat other things are they used for in number theory? #8548 20130226 09:53:32
Re: Linear Interpolation FP1 FormulaJust for the Fermat  Pell equation as far as I know. But these are an important class of diophantine equations. They are more important I think in numerical analysis. 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. #8549 20130226 10:55:29
Re: Linear Interpolation FP1 FormulaA girl asked me what I was doing today in chemistry, I was trying to solve a Pell equation using one of my CFs. When I tried to show her what a CF was, she said "I'd rather paint my nails". #8550 20130226 11:02:38
Re: Linear Interpolation FP1 FormulaYikes, an intellectual! 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. 