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continued-fraction expansion
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Continued fraction
11 Comparison of continued fractions; 12 Continued fraction expansions of π; 13 Generalized continued fraction; 14 Other continued fraction expansions ...
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While continued fractions are not the only possible representation of real numbers in terms of a sequence of integers (others include the decimal expansion and ...
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Jan 24, 2005 ... We say the continued fraction expansion of √2 is [1,2,2,2,...]. It is an example of an infinite continued fraction which every irrational number is.
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Continue the procedure until you obtain δ = 0. Example 2. Consider the continued fraction expansion for 42/31. We obtain a0 = [42/31] = 1, δ = 42/31 − 1 = 11/31.
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of a real number. It is the first step in the process of expanding x as a continued fraction. The process of finding the continued fraction expansion of a real number ...
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May 31, 2000 ... Every number has a continued fraction expansion but if we restrict our ambition only a little, to the continued fraction expansions of "almost ...
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This happens when the original number is rational, otherwise the procedure goes on forever... The compact notation used for the continued fraction expansion of ...
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Definition 1.2 The continued fraction expansion of a real number x is the sequence ... two numbers whose continued fraction expansions coincide must be equal.
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One of the interesting things about the continued-fraction expansion of (irrational) numbers is that they are, in a sense, base-independent. Instead of endlessly ...
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Let me emphasize that I am very new to sage and to computing in general, but I did research as much as I could before as.
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