is square root of 2 normally distributed?

[magomago]

This came to mind randomly as I've been helping some coworkers with normality.

Are the digits of ROOT(2) normal? I know its an irrational number, and it goes on forever, but does a distribution of the digits reveal is to be normal (in the traditional Gaussian sense)?

 

[Mr Evil]

They don't have a normal distribution, but √2 is probably (no one has proved it yet) a normal number, which means the digits have a uniform distribution.

 

[magomago]

root 2 is uniformly distributed?

 

[Mr Evil]

Yes.

 

[agent00f]

This came to mind randomly as I've been helping some coworkers with normality.

Are the digits of ROOT(2) normal? I know its an irrational number, and it goes on forever, but does a distribution of the digits reveal is to be normal (in the traditional Gaussian sense)?

How the hell are you helping anyone with normality or whatever when you don't know what a normal number is?

 

[Pulsar]

Yes.

OW.OW.OW.OW.OW.

Cut that shit out. It's worse that the cyst-popping video some douchebag linked to.

 

[C1]

ROOT(2) is categorized as being among the normal numbers (so far technically not formally provable) and its component distribution(s) show to be uniformly distributed.

 

[PianoMan]

This is so far beyond my engineering mathematics knowledge that I can see my own arsehole...

 

[Mike64]

OW.OW.OW.OW.OW.

Cut that shit out. It's worse that the cyst-popping video some douchebag linked to.

Huh?

 

[C1]

Maybe this helps:

A normal number is an irrational number for which any finite pattern of numbers occurs with the expected limiting frequency in the expansion in a given base (or all bases). For example, for a normal decimal number, each digit 0-9 would be expected to occur 1/10 of the time, each pair of digits 00-99 would be expected to occur 1/100 of the time, etc. A number that is normal in base-b is often called b-normal.

Determining if numbers are normal is an unresolved problem. It is not even known if fundamental mathematical constants such as pi (Wagon 1985, Bailey and Crandall 2003), the natural logarithm of 2 ln2 (Bailey and Crandall 2003), Apéry's constant zeta(3) (Bailey and Crandall 2003), Pythagoras's constant sqrt(2) (Bailey and Crandall 2003), and e are normal, although the first 30 million digits of pi are very uniformly distributed (Bailey 1988).

While tests of sqrt(n) for n=2 (Pythagoras's constant digits, 3 (Theodorus's constant digits, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15 indicate that these square roots may be normal (Beyer et al. 1970ab), normality of these numbers has (possibly until recently) also not been proven. Isaac (2005) recently published a preprint that purports to show that each number of the form sqrt(s) for s not a perfect square is simply normal to the base 2. Unfortunately, this work uses a nonstandard approach that appears rather cloudy to at least some experts who have looked at it.

http://mathworld.wolfram.com/NormalNumber.html

 

[PianoMan]

So in a statistical sense, we can see that irrational numbers approach being normal (like the example of pi above), but it hasn't been mathematically proven? Is that what we're talking about?

(Still OW.OW.OW.OW... )

 

[C1]

I think so.

Sounds (or reminds) like the idea of "limit" in calculus [eg, as x -> 0 then F(x) -> Some value.]. In this case, the "series expansion" is "any finite pattern of numbers" made up out of the subject irrational normal type number (number being sort of a misnomer).

Anyways, that's my take on it.

But like everyone says, this shit is too esoteric.


PS: Oh ya, I think one of the things confusing everyone is the use of the term "normal" in the problem discussion (eg, a normal number). It is suggestive of the term for a type of statistical distribution (ie, density function - normal distribution), but that misleads for this discussion.