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ON THE THEORY OF DIOPHANTINE APPROXIMATIONS AND CONTINUED FRACTIONS EXPANSION

Hailiza Kamarul Haili

Abstract


Approximation of irrational numbers by the rationals has been studied
for decades and one of the methods to approximate the irrationals is by
usrng the diophantine approximation and the convergents of its
continued fractions expansion Many results pertaining to this area of
research has been developed and documented. In 1963, Niven [Niv] in
his monograph had shown a sketch proof of several results related to
this problem. Now, in this paper we attempt to write a more
comprehensive and well sfuctured proofs. Given a real number 0,
how closely can it be approximated by rational numbers?.

Keywords: Diophantine approximatioq continued fractions, irrational
number, and rational number.

 

 


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