Degree Distasnce

[tom]

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

[C1ay]

Originally Posted by Robust

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.

[Damo2600]

Originally Posted by Qfwfq

Perhaps it's clearer to say:

angle = arc/radius

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

Even better:

arc = angle/radians

[Damo2600]

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.

[Robust]

Originally Posted by C1ay

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?

[C1ay]

Originally Posted by Robust

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.

[Robust]

Originally Posted by C1ay

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).

[Rincewind]

Originally Posted by Robust

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

Can you give us an example calculation showing how the two versions of the formula work, please C1ay and Robust?

Let's say using a radius of 7 cm and an angle of 0.48 rad (27.502°).

[C1ay]

Originally Posted by Rincewind

Can you give us an example calculation showing how the two versions of the formula work, please C1ay and Robust?

Let's say using a radius of 7 cm and an angle of 0.48 rad (27.502°).

Sure rince, 7*.48 = 3.36. Here's a chart I threw together to show the distance for each 10 degree marker around a unit circle, r=1.

Degrees	Radians	r*rad	r/radian
10	 0.1745	 0.1745	 5.7296
20	 0.3491	 0.3491	 2.8648
30	 0.5236	 0.5236	 1.9099
40	 0.6981	 0.6981	 1.4324
50	 0.8727	 0.8727	 1.1459
60	 1.0472	 1.0472	 0.9549
70	 1.2217	 1.2217	 0.8185
80	 1.3963	 1.3963	 0.7162
90 	 1.5708	 1.5708	 0.6366
100	1.7453	1.7453	0.5730
110	1.9199	1.9199	0.5209
120	2.0944	2.0944	0.4775
130	2.2689	2.2689	0.4407
140	2.4435	2.4435	0.4093
150	2.6180	2.6180	0.3820
160	2.7925	2.7925	0.3581
170	2.9671	2.9671	0.3370
180	3.1416	3.1416	0.3183
190	3.3161	3.3161	0.3016
200	3.4907	3.4907	0.2865
210	3.6652	3.6652	0.2728
220	3.8397	3.8397	0.2604
230	4.0143	4.0143	0.2491
240	4.1888	4.1888	0.2387
250	4.3633	4.3633	0.2292
260	4.5379	4.5379	0.2204
270	4.7124	4.7124	0.2122
280	4.8869	4.8869	0.2046
290	5.0615	5.0615	0.1976
300	5.2360	5.2360	0.1910
310	5.4105	5.4105	0.1848
320	5.5851	5.5851	0.1790
330	5.7596	5.7596	0.1736
340	5.9341	5.9341	0.1685
350	6.1087	6.1087	0.1637
360	6.2832	6.2832	0.1592

Notice that for r*radians the distances grow as the angle grows and for r/radians the distance shrinks as the angle grows. Perhaps robust can explain why the distance should be smaller for larger angles.

[tom]

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

We all agree on this, right?

The only problem is caused by robsts' notation. He calls 360 / 2pi radian. This is why his formula is

radius / radian

Originally Posted by Robust

No, Rincewind, the radian = 360-degrees/2pi. It is not determined by linear length (as is the radius).