1. ## pi question

just a theory I JUST came up with laying down trying to go to sleep. i haven't figured out all the details of it yet and i don't happen to have a supercomputer handy so i was hoping someone here could tell me...

ok... say we were to start a circle out with a radius of pi and a circumfrence of pi R2, as we calculate pi deeper and deeper into itself the circle grows and the wedge that is missing from the circumfrence (theoretically) shrinks now if we were to measure the distance of the missing wedge along the circumference, and the circumference itself minus the wedge, as the radius is kept equal to the Pi that we have calculated thus far, along with the area of both the circle minus the wedge and the wedge itself, could it be possible to find a constant or a variable in the rate of which the wedge would shrink grow or stay the same to prove whether or not Pi really is unending or not?

2. my birthday is pi day by the way that is why i have such a huge interest in this number.

3. nobody can help me?

4. Originally Posted by giinnocto
just a theory I JUST came up with laying down trying to go to sleep. i haven't figured out all the details of it yet and i don't happen to have a supercomputer handy so i was hoping someone here could tell me...

ok... say we were to start a circle out with a radius of pi and a circumfrence of pi R2, as we calculate pi deeper and deeper into itself the circle grows and the wedge that is missing from the circumfrence (theoretically) shrinks now if we were to measure the distance of the missing wedge along the circumference, and the circumference itself minus the wedge, as the radius is kept equal to the Pi that we have calculated thus far, along with the area of both the circle minus the wedge and the wedge itself, could it be possible to find a constant or a variable in the rate of which the wedge would shrink grow or stay the same to prove whether or not Pi really is unending or not?

RonL

5. ok start pi 3.14, there are still at least a million more place...

better example cut a distance in half then cut that half in half and continue, you never reach your destination... this is like the missing wedge in pi... if they measured the area and partial circumference avery time they added another digit to the pi that is the radius of the circle and the calculation of the circumference could they possibly figure whether or not pi really is unending by trying to find variables or consistencies in the area of the wedge and the partial circumference of the wedge as the radius grows and the calculation of the circumference gets calculated farther?

6. that is if the radius of a circle matched the calculation of pi each time we added another digit of pi in the calculation of finding the circumference we added a digit of pi to the radius so they matched.

7. Originally Posted by giinnocto
ok start pi 3.14, there are still at least a million more place...

better example cut a distance in half then cut that half in half and continue, you never reach your destination... this is like the missing wedge in pi... if they measured the area and partial circumference avery time they added another digit to the pi that is the radius of the circle and the calculation of the circumference could they possibly figure whether or not pi really is unending by trying to find variables or consistencies in the area of the wedge and the partial circumference of the wedge as the radius grows and the calculation of the circumference gets calculated farther?
$\displaystyle \pi$ is known (that is it is proven to be) irrational and transcendental. That means we know its decimal expansion is non-teminating and non-periodic (and for that matter its continued fraction expansion is known to be non-periodic).

RonL

8. Originally Posted by CaptainBlack
$\displaystyle \pi$ is known (that is it is proven to be) irrational and transcendental. That means we know its decimal expansion is non-teminating and non-periodic (and for that matter its continued fraction expansion is known to be non-periodic).

RonL

how did they prove that? i would like to know how it was proven.

9. Originally Posted by giinnocto
how did they prove that? i would like to know how it was proven.
Irrationality

Transendentality

RonL

10. Giinocto - I'm afraid that your explanation of how you're trying to show that pi is (or is not) irrational is impossible to follow. No offense, but I suggest you slow down, and use punctuation in your posts so that readers can follow your ideas a bit more clearly.

What I gather is that you want to consider a circle of radius pi, and then measure its circumference, which would be $\displaystyle C = 2*\pi^2$. Is that right? Are you thinking that as you measure the circumference one could perhaps see that it takes an infinite number of digits to measure it accurately? The problem is that all measurements of physical length have some degree of error. Perhaps using some really high-tech equipment you could measure the circumerence to an acuracy of, say, one millionth of an inch. The issue is that there are an infinite number of possible values of the true length of an object that lies within that millionth of an inch of uncertainty, and that infinite number of possible values inlcudes both an infinite number or rational numbers as well as an infinite number of irational values. Hence you can never prove by measuring something whether its length is a rational or irrational value. As a simpler example, consider this - draw a right angle triangle with legs of length 1, and then measure the hypotenuse. You know that the idealzed length of the hyptenuse would be $\displaystyle \sqrt 2$, which is an irrational number, but you can't prove that by simply measuring it. All you'd be able to say is that the hypotenuse is somewhere between about 1.414 and 1.415.

11. yea i cant work you through the proof but a rational number can be expressed by two integers m/n. its impossible to find an m/n = pi . and thats why it goes on forever

12. hereeeee you go...
Proof that π is irrational - Wikipedia, the free encyclopedia