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

enter image description here

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?

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

$$0.12345678910111213141516\dots$$

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

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