Moonchild Posted November 19, 2004 Report Posted November 19, 2004 OK...steradian and radian are variants of each other. Electricity and magnetism are variants of each other. Energy and matter are variants of each other. That's only slightly related to this string. The questjion:How does 2pi play in? What does it mean? When it's plugged into an equation, what does it do to that equation?
Tormod Posted November 19, 2004 Report Posted November 19, 2004 The short answer is that when calculating radians, 2pi is the same as 2piX withouth the X, which means you take out the dimension. So 2pi gives you a dimensionless value which is useful in all kinds of applications. And this I am quite sure is overly simplistic and needs some elaboration by our skilled members...
Bo Posted November 19, 2004 Report Posted November 19, 2004 almost always when an equation has a 2pi (or pi) in it, it has something to do with circular symmetries, but i dont really understand your question...Bo
Robust Posted November 19, 2004 Report Posted November 19, 2004 Perhaps the most essential use of 2 pi is that it relates the 360 degrees of a circle to its radian. Thus: 360/2 pi = radian.
Bo Posted November 20, 2004 Report Posted November 20, 2004 hmm essential is that 2pi is the circumference of the unit circle. and that some wiseguys decided that it then is convenient to define an anglemeasurement, for which a complete circle is 2pi radiansthe fact that this is equal to 360 degrees is completely trivial; it is just 2 quantities that are defined in the same way:2pi radians=360 degrees = 904.2 Ftwogl, where 1 Ftwogl is defined to be 1/(904.2) of the angular measurement. Bo
Robust Posted November 20, 2004 Report Posted November 20, 2004 Not trivial at all, Bo.....particularly as concerns mechanical engineering. Otherwise, it is the radian by which we are able to correlate distance on the arc with that of the radius which subtends it. Like root 2 - radian rules.
Aki Posted November 20, 2004 Report Posted November 20, 2004 Originally posted by: TormodThe short answer is that when calculating radians, 2pi is the same as 2piX withouth the X, which means you take out the dimension. So 2pi gives you a dimensionless value which is useful in all kinds of applications. Tormod, what do you mean by the dimensions?
FrankM Posted November 25, 2004 Report Posted November 25, 2004 The nomenclature related to 2 Pi is used to explain the characteristics of alternating current (AC) and/or electromagnetic signals. In the following URL, look in the section titled, "Angular Relationships of a Sinewave". Sinewaves
Robust Posted November 30, 2004 Report Posted November 30, 2004 And then there is just pi itself, a highly controversial subject in my quarters. I'm just a farmboy with no formal education, but it will take some doing to convince me that the area to any closed continuum can be defined by a ratio of line to arc that does not give either a whole figure or ending decimal. "All things number and harmony." - Pythagoras
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