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Old 04-20-2005   #1 (permalink)
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Degree Distasnce

One of the more frequently asked questions I get from graduate and undergraduate students alike is how to determine the distance between each angular degree on circumference of the circle. For those here who might ask, the answer is quite straightforward: radius/radian.
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Old 04-20-2005   #2 (permalink)
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Re: Degree Distasnce

Quote:
Originally Posted by Robust
One of the more frequently asked questions I get from graduate and undergraduate students alike is how to determine the distance between each angular degree on circumference of the circle. For those here who might ask, the answer is quite straightforward: radius/radian.
So let's make sure I understand you here. To make things easy let's use a unit circle so the radius=1. Now the distance halfway around the circle is pi radians so you're saying the distance between 0° and 180° on the circumference is 1/pi? The distance all the way around the circle is 1/2pi? One degree is pi/180 radians right? So the distance along one degree is 1/(pi/180)? Is this what you're saying?


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Old 04-20-2005   #3 (permalink)
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Re: Degree Distasnce

Quote:
Originally Posted by C1ay
So let's make sure I understand you here. To make things easy let's use a unit circle so the radius=1. Now the distance halfway around the circle is pi radians so you're saying the distance between 0° and 180° on the circumference is 1/pi? The distance all the way around the circle is 1/2pi? One degree is pi/180 radians right? So the distance along one degree is 1/(pi/180)? Is this what you're saying?
No, Clay. What I'm saying is exactly as stated: radius/radian = degree-distance. You give a radius of 1.0, so with a radian of 57.2957....then tthe distance between each angular degree on the circumference would be: 1/radian = 0.01745.... unit.
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Old 04-21-2005   #4 (permalink)
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Re: Degree Distasnce

i always though radians where between 0 and 2pi...

anyways, the definition is clear
distance on circle/angle = radius/angle

Bo
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Old 04-21-2005   #5 (permalink)
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Re: Degree Distasnce

Perhaps it's clearer to say:

angle = arc/radius

where angle will be given in radians, the ratio of two lengths.
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Old 04-21-2005   #6 (permalink)
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Re: Degree Distasnce

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Originally Posted by Bo
i always though radians where between 0 and 2pi...
They are. Robust is busy inventing new math again....


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Old 04-22-2005   #7 (permalink)
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Re: Degree Distasnce

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Originally Posted by C1ay
Robust is busy inventing new math again....
A noble activity, providing it's done properly.
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Old 04-22-2005   #8 (permalink)
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Re: Degree Distasnce

Quote:
Originally Posted by C1ay
They are. Robust is busy inventing new math again....
There's no new maths here at all, people. The radian is simply that distance on the arc as that of the radius which subtends it. Accordingly then, radius/radian gives the distance between each angular degree on the circumference.....as clearly shown by the given example.. I have given you new maths, but this certainly ain't it!
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Old 04-22-2005   #9 (permalink)
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Re: Degree Distasnce

Quote:
Originally Posted by Robust
No, Clay. What I'm saying is exactly as stated: radius/radian = degree-distance. You give a radius of 1.0, so with a radian of 57.2957...
Quote:
Originally Posted by Robust
The radian is simply that distance on the arc as that of the radius which subtends it. Accordingly then, radius/radian gives the distance between each angular degree on the circumference...
If the radian is the distance on the arc equal to the radius, then if the radius = 1, then the radian = 1, and radius/radian = 1, not 0.01745.
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Old 04-22-2005   #10 (permalink)
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Red face Re: Degree Distasnce

Quote:
Originally Posted by Rincewind
If the radian is the distance on the arc equal to the radius, then if the radius = 1, then the radian = 1, and radius/radian = 1, not 0.01745.
No, Rincewind, the radian = 360-degrees/2pi. It is not determined by linear length (as is the radius).
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