On the concept of optimality interval

Pelegrí Viader (), Jaume Paradís () and Lluís Bibiloni

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

Abstract: The approximants to regular continued fractions constitute `best approximations' to the numbers they converge to in two ways known as of the first and the second kind. This property of continued fractions provides a solution to Gosper's problem of the batting average: if the batting average of a baseball player is 0.334, what is the minimum number of times he has been at bat? In this paper, we tackle somehow the inverse question: given a rational number P/Q, what is the set of all numbers for which P/Q is a `best approximation' of one or the other kind? We prove that in both cases these `Optimality Sets' are intervals and we give a precise description of their endpoints.

Keywords: Diofantine approximations; continued fractions; metric theory (search for similar items in EconPapers)
JEL-codes: C00 (search for similar items in EconPapers)
Date: 2000-05
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Persistent link: https://EconPapers.repec.org/RePEc:upf:upfgen:466

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