Why will pi never repeat

Why will pi never repeat?

I know that how ever million places people have searched to it doesn't repeat, but why?

Other Answers:

Because that is the definition of an irrational number !

irrational number

A number that cannot be expressed as a ratio between two integers and is not an imaginary number.
If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition. ? and v2 are irrational numbers.

e is an irrational number, as well.

? and e are transcendental numbers. You can look that up...

? is ! There is no why !

QED

Because it is what is called an "irrational" number. In other words, it cannot be "rationalized', i.e. expressed as a ratio or a fraction. There is an infinite number of irrationals that exist between all the rational fractions.

Why can't it be expressed as a fraction? I think it's just a characteristic of our number system. Irrational numbers exist in the physical world. For example, the hypotenuse of a right triangle whose 2 shorter sides have a length of one. The hypotenuse is root 2 long, but you can only express root 2 as an unending, non repeating fraction.

http://www.po28.dial.pipex.com/maths/doc...

Let In(x)=o-1+1( 1-x2) ncos ( a x) dx

Integrating by parts we have

a 2In=2n( 2n-1) In-1-4n( n-1) In-2 ( n? 2)

which implies that

a 2n+1In=n!( Pnsin ( a ) +Qncos ( a ) ) (* )

where Pn,Qn are polynomials of degree <2n+1 in a with integer coefficients.

If it was to start repeating, that would be a mark of it being rational. But pi has been proven to be irrational, by definition, it cant repeat.