cap, i'll simplify it for you. i was right. circumference shrinks and radius doesn't. pi is not constant. happy birthday.

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.

pi=circumference/diameter, so even though it doesn't need to be 3.14........, it is still pi. and the ratio is not constant.

No, you aren't listening*. The constant Pi represents the circumference/radius ratio in circles with euclidean geometry.

 

 

 

 

* = reading.

so, pi only applies when it is stationary.

 

ok, if pi is no longer relavent when in motion, then if an angle is on the circle, does it's measure change?

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).

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

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.

but the measurement of angles (radians) is based on pi because it is the circumference/diameter

But the aplicvations of pi go beyond geometry. Is the identity below related to whetehr you do your maths in Euclidean space?:

 

[math]e^{\pi i} + 1 = 0[/math]

idk, but that has nothing to do with radians. radians were derived from this equation: [math]c=d{\pi}[/math]

I'm not talking about radians I'm talking about pi in general. Though we still use radians in GR.

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

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.

if the vertex is on the center of the circle, how is it euclidean?

rember as r -> 0 the ratio tends to pi.

remember radius doesn't shrink.

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.

i don't care. that isn't the point of the thread. it is off topic.

 

answer my question or don't post.

I answered your question, cos the 'circle' that we are considering is actually a point.

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?

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.

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

Yourdad doesn't seem to be understanding what Aeschylus is saying.

i seem to understand it is irrelavent and mostly already stated was incorrect in this scenario.