Approximation of Irrational Numbers

Martin Aigner
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Martin Aigner: Freie Universität Berlin, Fachbereich Mathematik und Informatik Institut für Mathematik

Chapter 1 in Markov's Theorem and 100 Years of the Uniqueness Conjecture, 2013, pp 3-29 from Springer

Abstract: Abstract Our story begins with one of the oldest questions in number theory: How well can a real number be approximated by rational numbers? Phrased in this way, the answer is “arbitrarily well,” since every real number α is the limit of a sequence $$(\frac{p_n}{q_n})$$ of rationals. But in such a convergent sequence, e.g., the decimal expansion of an irrational number α, the denominators usually grow very fast

Date: 2013
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DOI: 10.1007/978-3-319-00888-2_1

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