TY - JOUR
T1 - On the concept of optimality interval
AU - Bibiloni, Lluís
AU - Viader, Pelegrí
AU - Paradís, Jaune
PY - 2002/1/1
Y1 - 2002/1/1
N2 - The approximants to regular continued fractions constitute best approximations to the numbers they converge to in two ways known as 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. © 2002 Hindawi Publishing Corporation. All rights reserved.
AB - The approximants to regular continued fractions constitute best approximations to the numbers they converge to in two ways known as 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. © 2002 Hindawi Publishing Corporation. All rights reserved.
UR - https://www.scopus.com/pages/publications/17844392342
U2 - 10.1155/S0161171202011420
DO - 10.1155/S0161171202011420
M3 - Article
SN - 0161-1712
VL - 30
SP - 559
EP - 567
JO - International Journal of Mathematics and Mathematical Sciences
JF - International Journal of Mathematics and Mathematical Sciences
IS - 9
ER -