On rational approximations to irrational numbers

Series of Error Terms for Rational Approximations of Irrational Numbers

Let pn/qn be the n-th convergent of a real irrational number α, and let εn = αqn−pn. In this paper we investigate various sums of the type ∑ m εm, ∑ m |εm|, and ∑ m εmx m. The main subject of the paper is bounds for these sums. In particular, we investigate the behaviour of such sums when α is a quadratic surd. The most significant properties of the error sums depend essentially on Fibonacci nu...

On Irrational and Transcendental Numbers

Rational and Irrational Bubbles

Rational Approximations to n

Using an IBM 1130 computer, we have generated the first 20,000 partial quotients in the ordinary continued-fraction representation of x.

The rational approach to the irrational.

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