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1996•Journal of the Australian Mathematical Society Series A Pure Mathematics and StatisticsOpen access

Hall's ray in inhomogeneous diophantine approximation

Thomas W. Cusick, William Moran, Andrew D. Pollington

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Abstract

Abstract The aim of the paper is to show the existence of a ‘Hall's ray’ for the particular case of the one-sided inhomogeneous diophantine approximation problem, where the irrational is the golden ratio. The proof uses a sum-set method similar to that used by Marshall Hall for the original result of this kind.

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What this paper is about

Abstract The aim of the paper is to show the existence of a ‘Hall's ray’ for the particular case of the one-sided inhomogeneous diophantine approximation problem, where the irrational is the golden ratio. The proof uses a sum-set method similar to that used by Marshall Hall for the original result of this kind.

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Available abstract

Abstract The aim of the paper is to show the existence of a ‘Hall's ray’ for the particular case of the one-sided inhomogeneous diophantine approximation problem, where the irrational is the golden ratio. The proof uses a sum-set method similar to that used by Marshall Hall for the original result of this kind.

Key concepts: Diophantine approximation, Irrational number, Mathematics, Diophantine equation, Set (abstract data type), Hall effect, Diophantine set, Mathematical analysis

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