This is a post I read about pi while looking for stuff about tau -which is two times as much as pi.

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This makes me wonder, why does only pi contain such randomness? Don't other non-repeating and non-terminating numbers (like $sqrt(2)$) also have the same quality? Is this just a silly post that is only being biased towards pi, or is this random behavior only inherent to pi?


marked as duplicate by Ross Millikan, Did, user147263, user223391, Asaf Karagila Jun 27 '15 at 20:51

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    $\begingroup$ No, pi is just the go-to example of a transcendental/irrational number. There is currently no reason to consider the property, which it may or may not have, for pi specifically, versus some other transcendental. $\endgroup$ – Jonathan Hebert Jun 27 '15 at 13:14
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    $\begingroup$ In the sense of measure, almost all numbers have the property. But it is not known whether $\pi$ does! $\endgroup$ – André Nicolas Jun 27 '15 at 13:14
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    $\begingroup$ To expand @AndréNicolas's comment: this poster isn't saying much. Even if $\pi$ is a normal number (en.wikipedia.org/wiki/Normal_number) and has the properties cited on that poster, with probability $1$ any real number picked at random on the interval $[0,1]$ or $[0,10]$ or the whole real line is also normal and also has those properties. $\endgroup$ – Simon S Jun 27 '15 at 13:19
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    $\begingroup$ You can assume things all you want, but regarding your question, which is equivalent to "is it safe to say that pi is normal", the answer is a resounding no. The Goldbach conjecture has been confirmed for billions upon billions of numbers, but it's not safe to say that it is true, because if a mathematician hears you say that, you better be reaching for your proof. We do not say "[statement] is true" in mathematics, ever, unless we have a confirmed proof. $\endgroup$ – Jonathan Hebert Jun 27 '15 at 13:43
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    $\begingroup$ What @JonathanHebert said. Also: wouldn't it be interesting if it were shown that $\pi$ is not normal? $\endgroup$ – Simon S Jun 27 '15 at 13:45

The simplest example of a "universe" number is the Champernowne constant,


Among others, it contains the $n$ first decimals of $\pi$, for any $n$.


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