Second basic theorem of Hurwitz

We improve the well-known second theorem of Hurwitz from Diophantine approximation theory and prove that the numbers plus minus square root of two are the worst approximable among the irrational numbers when we omit the numbers that are equivalent to the golden ratio.

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Bibliographic Details
Published inLithuanian mathematical journal Vol. 56; no. 1; pp. 72 - 76
Main Author Hančl, Jaroslav
Format Journal Article
LanguageEnglish
Published New York Springer US 2016
Subjects
Actuarial Sciences
Mathematics
Mathematics and Statistics
Number Theory
Ordinary Differential Equations
Probability Theory and Stochastic Processes
Hurwitz’s theorem
approximation
continued fraction
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Summary:We improve the well-known second theorem of Hurwitz from Diophantine approximation theory and prove that the numbers plus minus square root of two are the worst approximable among the irrational numbers when we omit the numbers that are equivalent to the golden ratio.
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-016-9305-4