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 Entropy and The Randomness of The Digits of PI Commun. Korean Math. Soc. 2000 Vol. 15, No. 4, 683-689 Geon Ho Choe, Dong Han Kim Korea Advanced Institute of Science and Technology, Korea Advanced Institute of Science and Technology Abstract : The convergence rate of the expectation of the logarithm of the first return time $R_n$ with block length $n$ has been investigated for Bernoulli processes. This idea is applied to check the randomness of the digits of the decimal expansion of $\pi$, $e$ and $\sqrt{2}$. Keywords : the first return time, entropy, digits of $\pi$, ergodicity MSC numbers : Primary 37M25, secondary 94A17 Downloads: Full-text PDF