Dennisg Posted September 19, 2008 Author Posted September 19, 2008 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.
I_Pwn_Crackpots Posted September 19, 2008 Posted September 19, 2008 Can we talk about something else now?
ydoaPs Posted September 19, 2008 Posted September 19, 2008 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.
I_Pwn_Crackpots Posted September 19, 2008 Posted September 19, 2008 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!
ydoaPs Posted September 19, 2008 Posted September 19, 2008 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?
I_Pwn_Crackpots Posted September 19, 2008 Posted September 19, 2008 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.
ydoaPs Posted September 20, 2008 Posted September 20, 2008 Pi is dependent on the space. It is different in curved spaces. It is also different if the circle is spinning. Go ahead, provide a mechanism for the radius changing.
I_Pwn_Crackpots Posted September 20, 2008 Posted September 20, 2008 (edited) 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 September 20, 2008 by I_Pwn_Crackpots multiple post merged
insane_alien Posted September 20, 2008 Posted September 20, 2008 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.
Dave Posted September 20, 2008 Posted September 20, 2008 I meant to close this thread last night and forgot. PM me with objections.
Recommended Posts