Bazaar Question About Degrees And Radians..

[Iwonderaboutthings]

What I would love to understand as per the protocols of physics is:

 

 

For instant C = 2*pi, here we are left with divisions of zeros??

How can anything that travels in a straight path use such a method??

 

 

Does "radians" come in different lengths???

 

Meaning that are radians " straight lines" as if though beaming outward like photons??

 

 

Example x travels A to B, in a straight line with no curves whats so ever...

 

Is x straight distance from A to B considered the radian's distance in a straight line???

 

 

I found this converter link here, but somehow the straight line question does not seem to apply.

 

 

Degrees and radians

http://www.mathinary.com/degrees_radians.jsp

 

 

Several reasons I am confused on this is because:

 

Translation, The Unit Circle and Pi ratio which all involve empty space???

If so then how can radians be any length not = 0?

 

 

Sincerely confused

Edited September 12, 2013 by Iwonderaboutthings

[ajb]

For instant C = 2*pi, here we are left with divisions of zeros??

I don't follow. C= 2π is a real number, well defined and no problem.

 

A radian is an angular measurement, and what you are hinting at here is that 2π radians is equal to 360 degrees.

 

The defintion of a radiant is given by "An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle".

 

The improtant thing from this definition is that a radian is actually dimensionless. It comes from considering a ratio of lengths and so the units of the length used cancel. You might have to think about this carefully, but go through the definition explicitly.

[Iwonderaboutthings]

I don't follow. C= 2π is a real number, well defined and no problem.

 

A radian is an angular measurement, and what you are hinting at here is that 2π radians is equal to 360 degrees.

 

The defintion of a radiant is given by "An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle".

 

The improtant thing from this definition is that a radian is actually dimensionless. It comes from considering a ratio of lengths and so the units of the length used cancel. You might have to think about this carefully, but go through the definition explicitly.

Would you say that " although the units cancel that the numerical value is constant " somewhere not in the domains of space and time??

Hence 360 d, the speed of light, pi ratio etc

 

 

if the radian is = to the length " which one?" secant, cosec, cosine, tangent??

 

x or y, or does this not apply to the unit circle?

 

 

So if the units cancel out then there is no " real " method of getting the " single" radian and converting this to a single length with no curvature whats so ever?? Or would you just go back to the original length???

 

Its like going back and forth with converging, does not make sense at all and then the numerical values seem to get lost in all this but aren't the values just random numbers??

 

Could all this just be about position?

Hence: units cancel

Edited September 13, 2013 by Iwonderaboutthings

[ajb]

Would you say that " although the units cancel that the numerical value is constant " somewhere not in the domains of space and time??

It is a ratio, so it does not depend on the units used for the length. This does not have anything to do with space-time, you consider the mathematical situation of a circle and construct everything there. This then allows you use this as an angular measurement.

 

I am lost as to what this really has to do with physics.

 

 

The speed of light has dimensions "distence per time". It's numerical value will depend on the units employed.

 

if the radian is = to the length " which one?" secant, cosec, cosine, tangent??

 

x or y, or does this not apply to the unit circle?

 

Taken from: http://mathworld.wolfram.com/Radian.html

 

The above diagram defines one radian.

 

"The radian is a unit of angular measure defined such that an angle of one radian subtended from the center of a unit circle produces an arc with arc length 1"

 

 

It is the arc length used here and this does take into account "curvature".

 

 

http://en.wikipedia.org/wiki/Arc_length

 

 

 

So if the units cancel out then there is no " real " method of getting the " single" radian and converting this to a single length with no curvature whats so ever?? Or would you just go back to the original length???

One radian is dimensionless, it is in effect just a real number, but because of its definition it has some geometric meaning as an angular measurement.

 

 

 

Its like going back and forth with converging, does not make sense at all and then the numerical values seem to get lost in all this but aren't the values just random numbers??

Not random numbers, they are tied to the geometry.

Edited September 13, 2013 by ajb

[Iwonderaboutthings]

It is a ratio, so it does not depend on the units used for the length. This does not have anything to do with space-time, you consider the mathematical situation of a circle and construct everything there. This then allows you use this as an angular measurement.

 

I am lost as to what this really has to do with physics.

 

 

The speed of light has dimensions "distence per time". It's numerical value will depend on the units employed.

 

 

Taken from: http://mathworld.wolfram.com/Radian.html

 

The above diagram defines one radian.

 

"The radian is a unit of angular measure defined such that an angle of one radian subtended from the center of a unit circle produces an arc with arc length 1"

 

 

It is the arc length used here and this does take into account "curvature".

 

 

http://en.wikipedia.org/wiki/Arc_length

 

 

 

Thanks ajb this was very informative information and I will look into these links