/sci/ - Science & Math

It is tau/2.

pi is the 16th letter of the greek alphabet.

circumference = 2 * pi * r
pi = circumference / (2 * r) ~ 3. 1415 9265 3589 7932 3846 2643 3832 79

>>5831581
yes, but what makes pi what it is

you cannot just say where it is used. Its like a med student saying LEGS ARE FOR WALKING, not knowing how it works and why it works

Pi is the ratio of the diameter of a circle to its circumference. Measure the circumference and diameter of ANY circle, divide the circumference by the diameter, and you will get something roughly equal to pi.

>>5831591
what is the proof of pi?

>>5831594
>proof of pi

What does that mean?

>>5831603
that means how do we know that pi works considering that its a irrational number

most people just chirp that pi is just USED and its 22/7 but nobody really understands the core dynamics

>>5831609
It's not 22/7 that's an approximation

Pi works because it is a definition, pi is defined as the ratio of a circles circumference to its diameter. It's the same as 1 is defined as 1 or sqrt(2) is defined as sqrt(2). You'd never ask someone to prove that 4 is equal to 4 would you?

>>5831616

| | | | = | | | | <- up thats also for

^ yup thats four

there you go

>>5831609
the result is different: 22/7 is rational, pi is not.

>>5831609
>that means how do we know that pi works considering that its a irrational number

Pi is defined as the ratio of the circumference of a circle to its diameter. What do you mean by "works?"

If you're asking how to calculate the digits of pi, there are lots of ways.

https://en.wikipedia.org/wiki/Pi

>>5831619

I found this geometric proof here: http://www.slideshare.net/yaherglanite/estimating-pi

In slide nine, it looks like he suddenly assumes pi to prove pi. I don't think this is the case because of how pi is defined. We KNOW that it's the ratio between the circumference and the diameter, but we don't know the exact value. We can assume that since pi is the ratio, that the circumference must be the diameter times pi, no matter what the value of pi is. So this proof seems to check out ok.

>>5831627
demolished

you autistic retards, this is what OP wants

>>5831654
Does that mean Pi has an end?

>>5831669
acourding to the rules of geometry yes

to get long strings of "pi" you could just devide 22.000000000000....0000000000000001 with 7 and get that estimate number

>>5831669
It depends on what you mean by "end". The digits of pi go on infinitely, but it has a finite value. Essentially meaning that it's between 3.13 and 3.15. You can't really place pi exactly where it needs to go on a number line, since the best we can do is approximations. However, approximations can be fairly accurate, since the farther down the digits of pi you go, they become more and more trivialized, so the unaccounted for digits are hardly noticeable were you to place the approximation on a number line.

>>5831576
It's tasty, particularly when served as a dessert.

>>5831587
>pi = circumference / (2 * r) ~ 3. 1415 9265 3589 7932 3846 2643 3832 79

that's as detailed as you can get.

>>5831587
>not knowing THE DEFINITION of π

>>5831764
Don't go to that direction, anon: People will begin saying that pi is a natural occurrence on the circle, other people will say that pi was discovered and then we'll get into that argument about math being invented.

>>5831770
The accepted definition of pi is the ratio of the circumference of a circle to its diameter. Anyone who tries to argue differently is a bad troll.

>>5831779
implying there is only one good definition...
implying the ratio of the circumference of a circle to its diameter is still pi in other geometry ...

Define the complexe field, define the cosinus over C, pi/2 is the smallest positive real number in the kernel of cos.

>>5831576
Half of the circumference of a circle with a radius of 1, i.e a circle with a radius of oe has a circumference of 2pi, meaning that a circle's circumference can be determined by 2pir, because when r=1 the answer is 2pi

>>5831779
Lol, pi is defined by Euler's identity in 99% of mathematics. Physicist/Engineer detected.

>>5831616
or you could be silly and try to prove 1+1=2

One can also define pi as twice the unique root of cosx on the interval (0,2), first of course proving that it exists. This might be a more feasible definition for purposes of estimating it.

>>5833440
the original definition doesn't really matter when it comes to estimations since you usually dont use it to make calculations but an other formula which is more efficient.

the definition of pi with the cos is interesting because it's really easy to define the cosinus as a serie and to prove that there is only one root in [0;2]. If you define pi as a the ration of the circumference and the diameter of a circle you first have to define the lenght of a curve and so define intergrals and then to proov that this ratio is constant and ...

>>5833249
>Lol, pi is defined by Euler's identity in 99% of mathematics

no

>>5832011
>kernel of cos

Please don't use terminology you don't understand.

<div class="math">\pi=\frac{ln(-1)}{i}</div>

Can we all shut up now

>>5833536
at the begining i was thinking speaking of the complex exponential as a morphism from (C,+) to (C\{0},x) and define pi as the positive real number which satisfy <span class="math">2i \pi \mathbb{Z}=ker(exp)[/spoiler] then i changed my mind but for an unknow reason the word kernel stayed.

>>5833575
What the fuck did you wrote

>>5833584
Rearrangement of Euler's identity

>>5833575
or pi = iln(-1)

>>5833609
But that rearranges to

<div class="math">e^{\frac{\pi}{i}}=-1</div>

and that's wrong

>>5833616
That says e^(pi/i)

I am genus. I like fundamental constant pi and c

<span class="math"> c \approx 3*10^8 [/spoiler]

<span class="math"> \pi \approx 3 [/spoiler]

<span class="math"> \Longrightarrow c \approx \pi *10^8 [/spoiler]

Where is my prize?

>>5833616
1/i = -i
so
pi/i = -pi*i

>>5833626
ah I see, yeah that works

>>5831669
>Does that mean Pi has an end?
it approaches a limit

>>5833629
But then
i * ln(-1) = -i * ln(-1)
=> ln(-1) = 0 != pi
There's a problem somewhere.
I don't think you can rearrange Euler's identity just like that...

>>5833636
Fair enough I suppose

>>5833621
you mean <span class="math">\pi^2=g=9.84m \cdot s^{-2}[/spoiler] ? beat that others non-metric systems !

>>5833636
complex logarithm are a little more tricky than complex exponential

>>5833575
>http://en.wikipedia.org/wiki/Complex_logarithm#Problems_with_inverting_the_complex_exponential_function

>>5833651
>http://en.wikipedia.org/wiki/Lambert_W_function

>>5833652
that's some horrible shit right there