/sci/ - Science & Math

tell me /sci/, what the fuck does Pi have to do with probability distributions and expectations? Why is Pi in those sorts of formulas? What does average rainfall, which follows Gaussian distribution, have to do with circles?!?!

Why is Pi in sop many equations?!

I really suck at math is it anyway to improve it? I mean im not mentaly retarded or shit like that. I got 98% on english and did decent every other test, but I failed math 37% (you fail if the score is below 40%). So any tips?

>>8868300
But that's literally what pi is defined as: the ratio of a circle's circumference to its diameter. When he says "That's just what pi is," it sounds pretty hand-wavey, but that's really as fundamental as it gets.

The string 14977518 occurs at position 23165827. This string occurs 3 times in the first 200M digits of Pi.

14977518 = 14-9-7-7-5-18

14-9-7-7-5-18 = nigger

mind blown

How will you be celebrating it? (no pie answers ffs)

Math pleb who's trying to wrap his head around the infinity of π here.

Can any combination of numbers occur within it or are there restrictions? Because if anything goes doesn't that means at some point there is a near infinite string of 0s. Like graham's number amount of 0s for every digit that came before it, which would render anything that comes after it basically meaningless.

>Lemma: the sum of two rational numbers is rational.

Let x1=a/b and x2=c/d, where a, b, c, and d are integers. Then, x1+x2=a/b+c/d=ad/bd+bc/bd=(ad+bc)/bd. Since the product of two integers is an integer, and the sum of two integers is an integer, then x1+x2 is the ratio of two integers, and hence rational, completing the Lemma.

>Proof that pi is rational.

From calculus, we have the (admittedly slowly) converging series for pi: pi=4(1-1/3+1/5-1/7+1/9...). Since every term in the parenthesis is rational and being added together, by our lemma the term in parenthesis must be rational. Multiplication by four still leaves the result rational, and so pi is a rational number!

So, how many digits have pi?

Can a mathematician show that: In the number [math] \pi [/math] there will never be a repetition of the numeral 1 one thousand times in a consecutive fashion?

What is the largest repetition, found to date, in [math] \pi [/math]?

Is the statistical analysis of [math] \pi [/math] in terms of repetition a glimpse into a random number generator?

Did you all forget?

Anyone getting free pi at math departments today?

Let's say I have a number C that is both irrational and transcendental. Let's say I raise C to the value of a/b where 'a' and 'b' are whole integers. In other words:

C^(a/b)

Is there any way to prove that the number above is also an irrational and transcendental number?