2012•Experimental MathematicsOpen access

An Empirical Approach to the Normality of π

David H. Bailey, Jonathan Michael Borwein, Cristian S. Calude, Michael J. Dinneen, Monica E. Bad Dumitrescu, Alex Yee

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Abstract

Using the results of several extremely large recent computations [Yee and Kondo 11], we tested positively the normality of a prefix of roughly four trillion hexadecimal digits of π. This result was used by a Poisson process model of normality of π: in this model, it is extraordinarily unlikely that π is not asymptotically normal base 16, given the normality of its initial segment.

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Using the results of several extremely large recent computations [Yee and Kondo 11], we tested positively the normality of a prefix of roughly four trillion hexadecimal digits of π. This result was used by a Poisson process model of normality of π: in this model, it is extraordinarily unlikely that π is not asymptotically normal base 16, given the normality of its initial segment.

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Available abstract

Using the results of several extremely large recent computations [Yee and Kondo 11], we tested positively the normality of a prefix of roughly four trillion hexadecimal digits of π. This result was used by a Poisson process model of normality of π: in this model, it is extraordinarily unlikely that π is not asymptotically normal base 16, given the normality of its initial segment.

Key concepts: Normality, Local asymptotic normality, Mathematics, Asymptotic distribution, Poisson distribution, Normality test, Computation, Truncation (statistics)

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