ydoaPs Posted August 25, 2004 Author Posted August 25, 2004 cap, i'll simplify it for you. i was right. circumference shrinks and radius doesn't. pi is not constant. happy birthday.
Sayonara Posted August 25, 2004 Posted August 25, 2004 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.
ydoaPs Posted August 25, 2004 Author Posted August 25, 2004 pi=circumference/diameter, so even though it doesn't need to be 3.14........, it is still pi. and the ratio is not constant.
Sayonara Posted August 25, 2004 Posted August 25, 2004 No, you aren't listening*. The constant Pi represents the circumference/radius ratio in circles with euclidean geometry. * = reading.
ydoaPs Posted August 25, 2004 Author Posted August 25, 2004 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?
Aeschylus Posted August 25, 2004 Posted August 25, 2004 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).
ydoaPs Posted August 25, 2004 Author Posted August 25, 2004 but, pi isn't pi in this case, why would you use 3.14..........?
Aeschylus Posted August 25, 2004 Posted August 25, 2004 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.
ydoaPs Posted August 25, 2004 Author Posted August 25, 2004 but the measurement of angles (radians) is based on pi because it is the circumference/diameter
Aeschylus Posted August 25, 2004 Posted August 25, 2004 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]
ydoaPs Posted August 25, 2004 Author Posted August 25, 2004 idk, but that has nothing to do with radians. radians were derived from this equation: [math]c=d{\pi}[/math]
Aeschylus Posted August 25, 2004 Posted August 25, 2004 I'm not talking about radians I'm talking about pi in general. Though we still use radians in GR.
ydoaPs Posted August 25, 2004 Author Posted August 25, 2004 my question was if the measure of the angle changes. if it does, then you were wrong about always using 3.14.... for pi
Aeschylus Posted August 25, 2004 Posted August 25, 2004 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.
ydoaPs Posted August 25, 2004 Author Posted August 25, 2004 if the vertex is on the center of the circle, how is it euclidean?
Aeschylus Posted August 25, 2004 Posted August 25, 2004 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.
ydoaPs Posted August 25, 2004 Author Posted August 25, 2004 i don't care. that isn't the point of the thread. it is off topic. answer my question or don't post.
Aeschylus Posted August 25, 2004 Posted August 25, 2004 I answered your question, cos the 'circle' that we are considering is actually a point.
ydoaPs Posted August 25, 2004 Author Posted August 25, 2004 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?
Aeschylus Posted August 25, 2004 Posted August 25, 2004 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.
ydoaPs Posted August 25, 2004 Author Posted August 25, 2004 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
Cap'n Refsmmat Posted August 26, 2004 Posted August 26, 2004 Yourdad doesn't seem to be understanding what Aeschylus is saying.
ydoaPs Posted August 26, 2004 Author Posted August 26, 2004 i seem to understand it is irrelavent and mostly already stated was incorrect in this scenario.
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