# Degree Distasnce

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### #1 Robust

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Posted 20 April 2005 - 06:13 PM

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.

### #2 C1ay

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Posted 20 April 2005 - 07:36 PM

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?

### #3 Robust

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Posted 20 April 2005 - 11:10 PM

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.

### #4 Bo

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Posted 21 April 2005 - 03:42 AM

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

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

Bo

### #5 Qfwfq

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Posted 21 April 2005 - 03:48 AM

Perhaps it's clearer to say:

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

### #6 C1ay

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Posted 21 April 2005 - 04:48 AM

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

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

### #7 Qfwfq

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Posted 22 April 2005 - 06:01 AM

Robust is busy inventing new math again....

A noble activity, providing it's done properly.

### #8 Robust

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Posted 22 April 2005 - 11:41 PM

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!

### #9 Rincewind

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Posted 23 April 2005 - 12:29 AM

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...

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.

### #10 Robust

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Posted 23 April 2005 - 12:47 AM

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).

### #11 tom

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Posted 23 April 2005 - 04:08 AM

We all now that the length of an arc is

L = angle ( in radians ) * radius

angle ( in radians) = angle ( in degrees ) / 360 * 2 pi

L = angle ( in degrees ) / 360 * 2 pi * radius

We're talking about 1 degree so

L = 1 / 360 * 2 pi * radius

L = 2 pi / 360 * radius

360 / 2pi is the angle in degrees corresponding to an angle of 1 radian . To call this radian is not correct.
He says something true , but in his unique way

### #12 C1ay

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Posted 23 April 2005 - 03:33 PM

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!

Plenty of new math. A circle is 2π radians and the circumference of that circle is radius*2π not the radius/2π.

### #13 Damo2600

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Posted 24 April 2005 - 11:59 AM

Perhaps it's clearer to say:

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

Even better:

### #14 Damo2600

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Posted 24 April 2005 - 01:56 PM

Sorry that's wrong:

arc = radians / angle

IF angle is given as a fraction of 180 degrees.

degree distance = (pi)r / 180

Stuff it: radius / radians is much better.

### #15 Robust

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Posted 24 April 2005 - 06:14 PM

Plenty of new math. A circle is 2π radians and the circumference of that circle is radius*2π not the radius/2π.

You protest too quickly, Clay. The post does not relate to determining circumference but to the distance between each angular degree on the circumference - most readily given as radius/radian. Have you tried it?

### #16 C1ay

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Posted 24 April 2005 - 06:46 PM

You protest too quickly, Clay. The post does not relate to determining circumference but to the distance between each angular degree on the circumference - most readily given as radius/radian. Have you tried it?

Be it one degree or 360 of them, the distance is still the radius times the angle in radians, not the radius divided by the angle in radians.

### #17 Robust

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Posted 24 April 2005 - 11:43 PM

Be it one degree or 360 of them, the distance is still the radius times the angle in radians, not the radius divided by the angle in radians.

You got it just backwards, Clay. The distance between each angular degree on the circumference is given by radius/radian (as the quickest result).