Besicovitch, Bisection, and the normality of $0.(1)(4)(9)(16)(25)\dots$

Paul Pollack; Joseph Vandehey

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arXiv · 1405.6266

Besicovitch, Bisection, and the normality of $0.(1)(4)(9)(16)(25)\dots$

Paul Pollack·Joseph Vandehey

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Abstract

We revisit Besicovitch's 1935 paper in which he introduced several techniques that have become essential elements of modern combinatorial methods of normality proofs. Despite his paper's influence, the results he inspired are not strong enough to reprove his original result. We provide a new proof of the normality of the constant $0.(1)(4)(9)(16)(25)\dots$ formed by concatenating the squares, updating Besicovitch's methods.

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Paul Pollack, Joseph Vandehey. 2014-05-24. Besicovitch, Bisection, and the normality of $0.(1)(4)(9)(16)(25)\dots$. https://arxiv.org/abs/1405.6266

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