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A note on normality of $\sqrt{2}$ in base 2. (arXiv:1807.07338v1 [math.NT])
来源于:arXiv
In this paper we study the property of normality of a number in base 2. A
simple rule that associates a vector to a number is presented and the property
of normality is stated for the vector associated to the number. The problem of
testing a number for normality is shown to be equivalent to the test of
geometrical properties of the associated vector. The paper provides a general
approach for normality testing and then applies the proposed methodology to the
study of particular numbers. The main result of the paper is to prove that an
infinite class of numbers is normal in base 2. As a further result we prove
that the irrational number $\sqrt{2}$ is normal in base 2. 查看全文>>