Why is Pi infinite, sci? Why can't you calculate the area of a circle using a normal number?

Isn't that kind of a special case though? If i remember correctly Trigonometry is based on a circle with radius 1, and a right triangle with two legs being 1 is basically a quarter of that circle.

Nah man, other irrational numbers appear in trig too. You can get root(2) and root(3) from triangles too.

en.wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals

Well, what i meant is you calculate the are of the circle by thinking about it as smaller sqaures with the length of the radius. So obviously 3 squares are smaller than the circle, and 4 are bigger. So the 4th square gets broken into infinetely more smaller squares "to cover" to remaining area of the circle. These smaller squares are describes by pi minus 3.

But right triangles are just pieces of a circle.

Shapes are fucking my head man.

What you're trying to do is say that 4 squares of side length r (for radius) - an infinite number of smaller squares equals pi?

>Why can't you calculate the area of a circle using a normal number?
but you can. the result will be wrong though

No they're not.
You'd need an infinite number of infinitely small triangles to fill a circle directly.

Don't think of a circle as being "made up" of smaller shapes. That's where this confusion can come from.

Good old geometry can find irrational numbers like pi or root(2) from the ratios between side lengths of shapes.

The ratio of a circle's diameter to it's circumference is irrational.
The length of the hypotenuse of a triangle with short side length x is x*root(2).

But isn't any calculation using pi wrong by the degree that we don't know pi to?

It's inaccurate depending on how precise a value for pi you use.

The thing is, we can calculate pi for as long as we need it to, pretty easily. There are formulae that can calculate any decimal place of pi you like. You don't even need to know the decimals before it.

welcome to the wonderfully frustrating world of partial sums, user

Nah, 3 squares with the length r plus infinetely small brackets of one of those squares equal... well, not pi, but the area of the circle with the radius r. Since you now somehow have to calculate those infinietely small brackets you end up with pi sqaures. So basically, i think about Pi as 3 + an irrational number (with this irrational number obviously being pi minus 3). So this irrational number describes how many "parts" of a whole square you would need to describe the remaining area. And since you would need infinite infinietely small brackets of that square you end up with that irrational number. Hope that makes sense.

I guess, but I wouldn't recommend thinking about irrational numbers that way.

You shouldn't break up "irrational" shapes into infinitely many smaller shape.
Well, you can if you like. But it's not really that useful.

Could you draw what you mean?

>Why is Pi infinite
[math]|\pi | < 4 < \infty[/math]

they're a bit confused about irrationality, don't bite their head off

Well, I could, but I don't know if that would make it less confusing.

So let me rephrase it. You try to describe the area of a circle using squares. You take squares the length of the radius of the circle. You end up with it being a little more than 3 of these squares. This "a little more" is the percentage of a 4th square you need to fully cover the whole area of the square. So let's say in a parallel universe Pi is exactly 3,1. That would mean you need exactly 10% of the 4th square. In our universe though this "a little more" is an irrational number. And that is because what you need of the 4th square are infinitely small pieces.

So yeah my though basically was this. And the question that made me open this thread is could you not calculate that remaining area in some way that doesn't involve irrational numbers. Thank you.

*fully cover the whole area of the CIRCLE

Sounds like you're almost defining the way a limit works, or a convergent series.

We can actually do this. Image related is a formula that does this.

The problem is, this series only equals pi exactly if you let it run forever. If you stop it at any point, it's not equal to pi, just closer and closer to it.

So would you say it is correct if I imagine Pi to be 3 squares and the "percentage" of the 4th square?

And are there other ways to calculate the area of a circle?

Because so far I don't believe that circle really exist.

[math]3 < \pi < 4[/math]

Yeah, if you like. But the percentage of that 4th square is not a "nice" percentage to calculate or write down, if that makes sense. That percentage would probably still also be irrational (have an infinite number of digits).

There are other methods to calculate the area of a circle, but you always end up back at the same point: Area = pi*(Radius)^2. That is an invariant result.

You're identifying that a "perfect" circle cannot exist. You're correct. However, we can use enough digits of pi that we literally cannot measure the difference (I think it's around 50 digits is more than enough for any calculation).

>Because so far I don't believe that circle really exist.
Babby's first philosophy.

What does it mean to "perfectly exist"? Atoms can only get so close to a perfect geometrical shape. By that, ANY mathematically defined shape "doesn't really exist".

>DUDE PI IS INFINITE LMAO

I respect your trips, but i meant it doesnt even exist theoretically. Even theoretically you can only describe a shape with a lot of corners, how many depends on how many digits of pi you use. This is not true for the other shapes. Those have precise identities theoretically.

nah man, you can describe a circle perfectly using the ratio of diameter to circumference (pi).

Pi is an exact figure. it's decimal representation is infinitely long

Infinite =/= exact

The circle is a weird shape, maybe one day i will understand it.

Pi is an exact figure man. it's decimals are infinitely long, but we know what we are and can calculate as many as we like (around 100 million at least IIRC)

you can define Pi exactly as the ratio between the circumference and diameter of a shape drawn by the equation x^2+y^2=r^2

Because a true circle doesn't exist. Best you can do is calculate the surface area of an n-gon (perfect polygon with n sides) where n goes towards infinity. As you add more sides, they get smaller and the shape resembles a circle more and more. If Pi was finite, it would mean that a cricle is just an n-gon with a fixed amount of sides. But in reality, Pi is infinite because a circle is an abstract shape. You can always add more sides to an n-gon and you will never get a circle. Just like infinity - it's not a number, because you can simply increment any given number, resulting in a bigger number, meaning that the original number isn't infinity.

>ANY mathematically defined shape "doesn't really exist"
That's almost true, but...
An equipotential line around a point particle is perfectly spherical, and really exists.

Assuming point particles exist.

non-point particles still have point particles at their center

Because the area of a circle of radius 1 is infinity.

1-d particles, maybe, but if that resolution of the QM/GR conflict is accurate I'm not seeing the infinite subdivisions as being valid. As in, no point particles allowed.

that's not quite what i meant
if you wanted to describe the gravitational acceleration generated by an object, you would model that object's center of mass as a point particle. The object is not pointlike, but its center of mass is. And the equipotential surface around that object's center of mass in 3 dimensional space would be a perfect sphere regardless of the actual geometry of the object.

What's the probability of pi existing?

It comes down to perfect circles, an imaginary object, having infinite points.

In reality you would never need to use more than 3.14159.

Because circles dont actually exist

why don't you drop some matchsticks to find out

Makes you think that wildberger is on to something