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When Close Enough Is Close Enough
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0211-329
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2000-09-11
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The following equation is taken from my brother's algebra workbook. Sqrt(5-2*Sqrt(6))=Sqrt(3)-Sqrt(2)
He always challenges me to prove these equations like this by Mathematica, otherwise to remove this software to save disk space for his PC games. I am very lucky that Mathematica's FullSimplify[] function is powerful enough to solve these problems. But I am not sure whether what my brother brings next time may prove Mathematica a "failure."
After reading Edward R. Scheinerman's article "When Close Enough Is Close Enough" published on American Math Monthly June-July 2000, I know how to check equality "manually" if FullSimplify happens to fail. I implement a function according to Scheinerman's theory. In this Notebook, CalculateEquality[] is such a function. You can check the equality of algrebraic integers (roots of some monic, integer polynomial) by numerical calculation.
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implementing functions, FullSimplify
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| ReadMe.txt (826 B) - ASCII-Text | | Close.nb (25 KB) - Mathematica Notebook |
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