Introduction to Diophantine Approximation

• Autorzy: Yasushige Watase
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

irrational number; approximation; continued fraction; rational number; Dirichlet’s proof

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2015
• Tom: 23
• Numer: 2
• Strony: 101-106

Daty

wydano

2015-06-01

otrzymano

2015-04-19

online

2015-08-13

Twórcy

autor

Yasushige Watase

• Suginami-ku Matsunoki 6 3-21 Tokyo, Japan

Bibliografia

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Identyfikatory

DOI

10.1515/forma-2015-0010