Displaying similar documents to “An objective and practical method for describing and understanding ratios”

It’s not that they couldn’t

Reviel Netz (2002)

Revue d'histoire des mathématiques

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The article offers a critique of the notion of ‘concepts’ in the history of mathematics. Authors in the field sometimes assume an argument from conceptual impossibility: that certain authors could not do X because they did not have concept Y. The case of the divide between Greek and modern mathematics is discussed in detail, showing that the argument from conceptual impossibility is empirically as well as theoretically flawed. An alternative account of historical diversity is offered,...

Tong’s spectrum for Rosen continued fractions

Cornelis Kraaikamp, Thomas A. Schmidt, Ionica Smeets (2007)

Journal de Théorie des Nombres de Bordeaux

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In the 1990s, J.C. Tong gave a sharp upper bound on the minimum of k consecutive approximation constants for the nearest integer continued fractions. We generalize this to the case of approximation by Rosen continued fraction expansions. The Rosen fractions are an infinite set of continued fraction algorithms, each giving expansions of real numbers in terms of certain algebraic integers. For each, we give a best possible upper bound for the minimum in appropriate consecutive blocks of...

Continued fraction expansions for complex numbers-a general approach

S. G. Dani (2015)

Acta Arithmetica

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We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the...