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Hailiza Kamarul Haili
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Mathematics

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ON THE THEORY OF DIOPHANTINE APPROXIMATIONS AND CONTINUED FRACTIONS EXPANSION Hailiza Kamarul Haili
Proceedings of ICMSA Vol 1, No 1 (2005): ICMSA 2005
Publisher : Proceedings of ICMSA

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Abstract

Approximation of irrational numbers by the rationals has been studiedfor decades and one of the methods to approximate the irrationals is byusrng the diophantine approximation and the convergents of itscontinued fractions expansion Many results pertaining to this area ofresearch has been developed and documented. In 1963, Niven [Niv] inhis monograph had shown a sketch proof of several results related tothis problem. Now, in this paper we attempt to write a morecomprehensive and well sfuctured proofs. Given a real number 0,how closely can it be approximated by rational numbers?.Keywords: Diophantine approximatioq continued fractions, irrationalnumber, and rational number.  
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