"Turn and fly heading 3/4π rad" 

It seems to be common, at least in my country, to measure angles in a unit known as "the degree". This is unfortunate as the degree in truly a primitive and barbaric unit of angular measure. Supposedly, its origins lie in the fact that ancient cultures divided the year into 360 days so the degree divides the circle into 360 segments. This is quite a poor way to do mathematics. 

Last edited by PhilosopherStoned; 01172011 at 07:00 AM.
Previously PhilosopherStoned
"Turn and fly heading 3/4π rad" 

0.750 pirad; sounds cool to me. 

Well from a practical, nonmathematical perspective, you would probably want to do something like change units to degrees because factors of 360 are easy to work with but the introduction to angular measure should be radians. You should just think of 1 degree as π/180 radians. All I'm saying is that the radian is the natural unit of circular measure and I don't think it's pedagogically right to introduce a contrived unit before a natural one. 

Last edited by PhilosopherStoned; 01182011 at 02:14 AM.
Previously PhilosopherStoned
I didn't exactly understand the part about string. Is that supposed to be some elementary school trick? I was never taught about radians, although I do they are the "real" measuring unit when it comes to angles. It can be quite frustrating when working with MathCad, because it outputs a lot of things in radians. 


Lost count of how many lucid dreams I've had

Imagine a string going from the center of a circle to the edge. So the string denotes the radius. Now imagine wrapping that same radiuslength piece of string around the circumference of the circle. That's a radian. 

Basically think of any angle as describing a segment of a circle, and then radians measure how many radii fit into along the edge of the circle. 

The only problem is that there isn't an even (or even rational) amount of radians in a circle, which is probably why they don't teach them to 4th graders. 

Uhm, where the hell did you get the info that the 360 has anything to do with the number of days in a year? They chose 360 because it's divisible by a lot of things evenly: 2, 3, 4, 5 ,6 ,8, 9, 10, 12, 15, 18, 20, 30, 45, 60, 90, and 180. 

I don't see why it's a problem for students that the number of radians in a circle isn't nice and simple. You don't usually need to measure the angle of a circle... 

I don't think that's a valid complaint. If I'm not wrong, they teach the formula c = 2πr to fourth graders. Then it's just division to get that half of a circles angle is 2πr/2 = πr. But we can then divide both sides by r. 

Previously PhilosopherStoned
The thing is degrees are generally taught in basic geometry to measure angles within different polygons and shapes. Using rads for that would be incredibly tedious. 

Ah, I see, it all makes a lot of sense then. 


Lost count of how many lucid dreams I've had

Straight line: 1 pirad, 180 degrees. 

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