The Classification of Rational Appoximations
Percy J. Heawood · Proceedings of the London Mathematical Society · 1922
Cb ( # 7 1 + 1 > & N + 2> &71 + 3 , • • • ) » * 2/1/ in his notation: then the least value of L </D is the minimum of the form.I Or if a,, + i = 1, in any case.* I.e.representing 2's in the fractions compared in (b), (c), not necessarily in the original fraction owing to transformations.See the end of § 3.t This is a question not definitely considered by Markoff.J It should hardly be necessary to emphasise that these 2's are not the digits of the continued fraction, but the numbers of successive l's and 2's of which these digits consist.* MarkofE only shows explicitly the case of the 2's occurring in doublets, though the possible vanishing of certain numbers which he uses involves the other case.+ Not necessarily representing l's in the original fraction, as noted in §4.