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- ...e, surely, can make the difference between <math>x</math> and its rational approximation <math>\frac pq</math> as small as we wish. The problem is that, as we try t So, the interesting question is whether we can get a smaller error of approximation than <math>\frac 1q</math>. Surprisingly enough, it is possible, if not for7 KB (1,290 words) - 11:18, 30 May 2019
- '''Rational approximation''' is the application of [[Rational approximation|Dirichlet's theorem]] which shows that, for each irrational number <math>x\ ...er|Liouvillian]]. It can be read right after its parent article [[rational approximation of famous numbers]]. The proof of the non-Liouvillian character of <math>\l8 KB (1,431 words) - 12:48, 26 January 2008
- ...associated with the approximation; provided the error is small enough, the approximation will not be significantly worse than an exact solution. A survey of some approximation techniques follows.2 KB (322 words) - 20:03, 11 February 2009
- #REDIRECT [[Rational approximation#Liouville Approximation Theorem]]68 bytes (6 words) - 22:59, 4 April 2009
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- ...etimes considered to be divided into the areas of [[Dynamical Systems]], [[Approximation Techniques]], and [[Probability]] & [[Statistics]]. There are also various6 KB (902 words) - 17:16, 22 October 2024
- === Example 1: Rational Approximation Theorem ===11 KB (1,986 words) - 18:13, 19 June 2024
- A '''Riemann sum''' is a finite approximation to the [[Integral|Riemann Integral]].1 KB (272 words) - 11:06, 7 May 2008
- ...o Hata. This article can be read right after its parent article [[rational approximation of famous numbers]], but an unexperienced reader may prefer to read the pro ...<math>0</math> and <math>1</math>. Using the main theorem from [[rational approximation of famous numbers|the parent article]], we see that it remains only to show8 KB (1,469 words) - 20:11, 16 September 2022
- ...ingle-variable case) such that <math>h'(x) \cdot \Delta x</math> is a good approximation to <math>h(x+ \Delta x) - h(x)</math>. Thus, it seems that <math>f'(g(x))12 KB (2,377 words) - 10:48, 22 July 2009
- ...n Value Theorem, fortunately, gives us exact equality, rather than just an approximation.)11 KB (2,082 words) - 14:23, 2 January 2022
- * [[Rational approximation]]1 KB (207 words) - 14:51, 25 August 2022
- * The [[Rational_approximation#Liouville_Approximation_Theorem | Liouville Approximation Theorem]] provides one way of showing that certain numbers are transcendent568 bytes (72 words) - 10:52, 9 December 2007
- ...e, surely, can make the difference between <math>x</math> and its rational approximation <math>\frac pq</math> as small as we wish. The problem is that, as we try t So, the interesting question is whether we can get a smaller error of approximation than <math>\frac 1q</math>. Surprisingly enough, it is possible, if not for7 KB (1,290 words) - 11:18, 30 May 2019
- An approximation for Euler's number is <math>e\approx 2.7182818284590452...</math>4 KB (764 words) - 20:09, 13 March 2022
- ==Proof via Dirichlet's simultaneous [[rational approximation]] theorem==2 KB (333 words) - 12:50, 26 June 2006
- '''Rational approximation''' is the application of [[Rational approximation|Dirichlet's theorem]] which shows that, for each irrational number <math>x\ ...er|Liouvillian]]. It can be read right after its parent article [[rational approximation of famous numbers]]. The proof of the non-Liouvillian character of <math>\l8 KB (1,431 words) - 12:48, 26 January 2008
- If <math>s^2=85-42\sqrt{2}</math>, using <math>1.4</math> as an approximation for <math>\sqrt{2}</math>, <math>s^2\approx 85-42\cdot 1.4=85-58.8=26.2</ma7 KB (1,182 words) - 13:31, 1 September 2024
- ...6</math>. It is desired to replace each <math>a_i</math> by an [[integer]] approximation <math>A_i</math>, <math>1\le i \le 7</math>, so that the sum of the <math>A2 KB (377 words) - 01:17, 16 February 2021
- ...ncreasing for positive reals while its derivative is decreasing, so linear approximation gives4 KB (673 words) - 18:48, 28 December 2023
- ...\frac 13, \frac 14</math> anyway. For <math>\frac 27</math> to be the best approximation for <math>r</math>, the decimal must be closer to <math>\frac 27 \approx .21 KB (208 words) - 10:46, 4 June 2021
- We can make an approximation by observing the following points: ...\frac{1}{60}</math> in degrees, convert to radians and use the small angle approximation <math>\sin(x)=x</math>.3 KB (469 words) - 20:14, 7 July 2022
- with the first approximation from the definition of the partial derivatives9 KB (1,537 words) - 20:04, 26 July 2017
- ...2.86</math>. It is desired to replace each <math>a_i</math> by an integer approximation <math>A_i</math>, <math>1\le i \le 7</math>, so that the sum of the <math>A7 KB (1,071 words) - 18:24, 23 February 2024
- ...test for equality within <math>10^{-5}</math> ps points in order to avoid approximation errors.3 KB (532 words) - 09:48, 4 October 2024