Best Rational Approximation Calculation Utility For Windows
The console-mode utility supplied on this page is also included in the ESRG Tool Set download (along with many, many other rational approximation goodies), but it is quicker and easier to grab the utility and supporting mathematical documentation here if that is all you require.
The utility was created using Microsoft Visual C++ 6.0, and has no external dependencies (no .DLL dependencies, for example). It should run on any Windows 95 or later system.
The screen snapshot below shows the utility being used to find the best rational approximation to p (or actually, to 3.14159265359 since p is irrational) with numerator not exceeding 65,535 and denominator not exceeding 32,767. The screen snapshot shows that this best rational approximation is 65,298/20,785.
The underlying algorithms are O(log N) and an arbitrary-precision integer library is used, so they should work for any practical case.
This standalone utility and other supporting documents can be downloaded from the links in the table below.
Download Link | Description | File Size And MD5 |
cfbrapab.exe | Windows utility to calculate best rational approximations. | Size: 81,920 MD-5 02c8738054c23445a69bd0d675ceca0a |
paper_brap_detailed.pdf | Detailed paper explaining the mathematical basis of best rational approximation. (Note: this paper was never published, and copyrights do not apply.) | Size: 273,133 MD-5: fea545ffe55e1c1ef639f93eb844e0bb |
paper_brap_reduced.pdf | Less detailed paper explaining how to calculate best rational approximations. (Note: this paper was never published, and copyrights do not apply.) | Size: 152,959 MD-5: cdd7b25e94c4c304315002eb858a125d |
book_c4_c5.pdf | Chapters 4 (Farey Series) and 5 (Continued Fractions) of book, under construction. This document gives much more detail about the mathematical basis of best rational approximation. (Note: the copyright status of the book is uncertain. For the present time, no copyrights apply.) | Size: 631,559 MD-5: 87e410eb524ad5dd0e8011f5567f9e30 |
Other notes:
Sound
credit: George Carlin, Parental Advisory.
This
page maintained by David T.
Ashley.
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