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04-20-2005
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#1 (permalink)
| | Suspended |
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. | |
04-20-2005
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#2 (permalink)
| | ¿42? |
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? 
---------------- Clay Editor and Forum Administrator stego anyone?
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04-20-2005
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#3 (permalink)
| | Suspended |
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. | |
04-21-2005
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#4 (permalink)
| | Understanding |
Re: Degree Distasnce i always though radians where between 0 and 2pi...
anyways, the definition is clear 
distance on circle/angle = radius/angle
Bo | |
04-21-2005
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#5 (permalink)
| | Exhausted Gondolier |
Re: Degree Distasnce Perhaps it's clearer to say:
angle = arc/radius
where angle will be given in radians, the ratio of two lengths. | |
04-21-2005
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#6 (permalink)
| | ¿42? |
Re: Degree Distasnce Quote: |
Originally Posted by Bo i always though radians where between 0 and 2pi... | They are. Robust is busy inventing new math again....
---------------- Clay Editor and Forum Administrator stego anyone?
Add yourself to Hypography's Frappr. "There are only 10 kinds of people in the world -- .....Those who understand binary, and those who don't."
"Draw no conclusions before their time." | |
04-22-2005
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#7 (permalink)
| | Exhausted Gondolier |
Re: Degree Distasnce Quote: |
Originally Posted by C1ay Robust is busy inventing new math again.... | A noble activity, providing it's done properly. | |
04-22-2005
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#8 (permalink)
| | Suspended |
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! | |
04-22-2005
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#9 (permalink)
| | Questioning |
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. | |
04-22-2005
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#10 (permalink)
| | Suspended |
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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