Pi

[foodchain]

I was reading up on pie and it sounded good to eat, no that was a bad joke.

 

Ok, I was reading on pi and I was wondering if the reason people cant get an exact number, or something other then irrational is due to the shape of the circle. Such as a circle, or its circumference lacks a point, or is sort of always in a curve regardless of position in regards to circumference.

[the tree]

There is an exact value for pi, it's just not a rational one. And yes, pi is defined by the shape of the circle, I have no idea what you were speculating in regards to there.

[Bignose]

Yeah, the tree said it right, pi has an exact number, it just isn't rational. Proofs of its irrationality have been around for quite some time, I am sure you can find several by using your favorite web search engine.

[ajb]

Such as a circle, or its circumference lacks a point, or is sort of always in a curve regardless of position in regards to circumference.

 

The circle is an exmple of what is known as a "manifold". As such you can always define a "point" on that manifold using (local) coordinates.

 

You can just use your embedding of the circle in [math]\mathbb{R}^{2}[/math] to define local coordinates, i.e [math](x,y)[/math] such that [math] x^{2} + y^{2} = 1[/math].