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Is a circle spinning near c still a circle?  

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  1. 1. Is a circle spinning near c still a circle?



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That's not actually true. You need to re-read what was said earlier.

 

Pi is defined as a part of plane geometry. When you reduce the circumference but not the radius, the circle is no longer Euclidean - the circumference-radius ratio does not need to be pi.

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It's a matter of defintion, read these (notice the firstone delibartely avoids saying thta pi is not constant):

 

http://www.google.com/url?sa=U&start=1&q=http://mathforum.org/library/drmath/view/55021.html&e=747

 

http://mathforum.org/library/drmath/view/58292.html

 

If you ever see the number pi in any equation, even one that descirbes a non-Euclidea space you can be sure that it will be the pi that we're famlair wtih (i.e. the one defined by plane geometry).

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but, pi isn't pi in this case, why would you use 3.14..........?

 

because pi as in 3.14... is an important mathematical constant whichever way you look at it and pi has uses far beyond describing the ratio of the diameter of a circle to it's circunference.

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my question was if the measure of the angle changes. if it does, then you were wrong about always using 3.14.... for pi

 

The way angles are measured doesn't change. The kind of spaces we are talking about are Rimeannian manifolds and they are 'locally' Euclidean.

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remember radius doesn't shrink.

 

I think your getting confused, I'm not talking about the specific example of the relatvistic disc, I'm talking about circles in spatial slices of the Lorentzian metrics of GR. For an equation describing the circle as the parameter r (the radius) tends to zero, the ratio between the circle's diameter to it's circumference tends to pi.

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no, it isn't. the radius DOES NOT SHRINK, so it wouldn't be a point. did you not read the last few pages of this thread?

 

Have you?

 

We're talking about angles between lines which are defined by the point where they intersect not by a circle.

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no, we are talking about a positive angle drawn on circle with the vertex being the center. my question is, scince pi is no longer 3.14...... dos the measurement change. you keep using arguments we have already stated are wrong. please stop

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