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About: Ostrowski numeration     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatNon-standardPositionalNumeralSystemsyago:Artifact100021939yago:Instrumentality103575240yago:Object100002684yago:PhysicalEntity100001930yago:System104377057yago:Whole100003553 New Facet based on Instances of this Class

In mathematics, Ostrowski numeration, named after Alexander Ostrowski, is either of two related numeration systems based on continued fractions: a non-standard positional numeral system for integers and a non-integer representation of real numbers. Fix a positive irrational number α with continued fraction expansion [a0; a1, a2, ...]. Let (qn) be the sequence of denominators of the convergents pn/qn to α: so qn = anqn−1 + qn−2. Let αn denote Tn(α) where T is the Gauss map T(x) = {1/x}, and write βn = (−1)n+1 α0 α1 ... αn: we have βn = anβn−1 + βn−2.