# Introduction to Diophantine Approximation

Formalized Mathematics (2015)

- Volume: 23, Issue: 2, page 101-106
- ISSN: 1426-2630

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topYasushige Watase. "Introduction to Diophantine Approximation." Formalized Mathematics 23.2 (2015): 101-106. <http://eudml.org/doc/271783>.

@article{YasushigeWatase2015,

abstract = {In this article we formalize some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals. A typical example is finding an integer solution (x, y) of the inequality |xθ − y| ≤ 1/x, where 0 is a real number. First, we formalize some lemmas about continued fractions. Then we prove that the inequality has infinitely many solutions by continued fractions. Finally, we formalize Dirichlet’s proof (1842) of existence of the solution [12], [1].},

author = {Yasushige Watase},

journal = {Formalized Mathematics},

keywords = {irrational number; approximation; continued fraction; rational number; Dirichlet’s proof; Dirichlet's proof},

language = {eng},

number = {2},

pages = {101-106},

title = {Introduction to Diophantine Approximation},

url = {http://eudml.org/doc/271783},

volume = {23},

year = {2015},

}

TY - JOUR

AU - Yasushige Watase

TI - Introduction to Diophantine Approximation

JO - Formalized Mathematics

PY - 2015

VL - 23

IS - 2

SP - 101

EP - 106

AB - In this article we formalize some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals. A typical example is finding an integer solution (x, y) of the inequality |xθ − y| ≤ 1/x, where 0 is a real number. First, we formalize some lemmas about continued fractions. Then we prove that the inequality has infinitely many solutions by continued fractions. Finally, we formalize Dirichlet’s proof (1842) of existence of the solution [12], [1].

LA - eng

KW - irrational number; approximation; continued fraction; rational number; Dirichlet’s proof; Dirichlet's proof

UR - http://eudml.org/doc/271783

ER -

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