18/01/09 23:29:48.09 Xw3gWI4S.net
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"Irrationality measure"について
URLﾘﾝｸ(en.wikipedia.org)
Liouville number
(抜粋)
6 Irrationality measure
The irrationality measure (or irrationality exponent or approximation exponent or Liouville?Roth constant) of a real number x is a measure of how "closely" it can be approximated by rationals. Generalizing the definition of Liouville numbers, instead of allowing any n in the power of q, we find the least upper bound of the set of real numbers μ such that
0< |x-p/q|< 1/q^μ
is satisfied by an infinite number of integer pairs (p, q) with q > 0. This least upper bound is defined to be the irrationality measure of x.[3]:246
(引用終り)
URLﾘﾝｸ(mathworld.wolfram.com)
Irrationality Measure MathWorld Wolfram Research, Inc.
URLﾘﾝｸ(planetmath.org)
irrationality measure planetmath.org Owner: mathcam Added: 2004-02-27 - 13:34 Author(s): mathcam Versions (v8) by mathcam 2013-03-22
(畑 政義先生)
URLﾘﾝｸ(projecteuclid.org)
URLﾘﾝｸ(projecteuclid.org)
Improvement in the irrationality measures of π and π^2 Masayoshi Hata Proc. Japan Acad. Ser. A Math. Sci. Volume 68, Number 9 (1992), 283-286.
URLﾘﾝｸ(www.math.kyoto-u.ac.jp)
畑 政義 京都大学 理学研究科／理学部 数学教室