Degree Distasnce

[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.

[C1ay]

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?

[Robust]

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.

[Bo]

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

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

Bo

[Qfwfq]

Perhaps it's clearer to say:

angle = arc/radius

where angle will be given in radians, the ratio of two lengths.

[C1ay]

Originally Posted by Bo

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

They are. Robust is busy inventing new math again....

[Qfwfq]

Originally Posted by C1ay

Robust is busy inventing new math again....

A noble activity, providing it's done properly.

[Robust]

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!

[Rincewind]

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...

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.

[Robust]

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).