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Can pi be reduced to a rational number?


Dennisg
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Bearing this in mind, the answer to your question is: no, is irrational because it is a mathematical definition

 

One point here is that the current definition breaks down with circles where d = planks length because r no longer exists.

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And so will the radius. As such, pi is always irrational.

 

NO! The length of the radius is perpendicular to the direction of motion.

 

Say this circle is a merry-go-round. You are on the edge, spinning at relativistic speed, and you are trying to measure the circumference with a ruler (the circle is large enough that this isn't completely foolish). The ruler would contract, and therefore more ruler lengths would fit around the outside. You would measure the ratio to be larger than pi.

 

Maybe this is a question of reference frames, though. In a rest frame, the circumference would contract. No such specification was made in the original post, however.

The length of the circumference would shrink just as much as the ruler. You would measure it to be the same. You're mixing frames here.
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NO! The length of the radius is perpendicular to the direction of motion.

 

So what?

 

Don't you remember that C= 2*(pi)*r ?

 

If the circumference decreases, so does the radius. It doesn't matter what the speed is, or which direction it is going at. End of story. Nothing changes. We can all sing along. I'm bored.

 

NEXT!

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So what?

 

Don't you remember that C= 2*(pi)*r ?

 

If the circumference decreases, so does the radius. It doesn't matter what the speed is, or which direction it is going at. End of story. Nothing changes. We can all sing along. I'm bored.

 

NEXT!

You do know that is just a rearranged form of the definition of [math]\pi[/math], right?

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You do know that is just a rearranged form of the definition of [math]\pi[/math], right?

 

I am aware of that. The point is, is that [math]\pi[/math] doesn't change, and the length of the circumference is completely dependent on the length of the radius. It doesn't make any sense to talk about changing the circumference without changing the radius too.

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True, but special relativity doesn't leave Euclidean space, now does it? General relativity does. But then, the definition and the formula of a circle is something else in non-euclidean surfaces.

 

EDIT: You just changed what you typed down. oh well.

 

Conclusion, pi is not rational. Period. You can spin it as fast as you like or deform it all you want, but pi and the formula for the circumference is a mathematical definition and is not going to change.

Edited by I_Pwn_Crackpots
multiple post merged
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I_Pwn_Crackpots, YDOAPS didn't change what he wrote otherwise there would be an edit tag on it.

 

and he is right, special relativity causes things to contract in the direction of motion not perpendicular to that. so a spinning circle would stay the same radius but have a contracted circumference.

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