In some contexts it makes sense to talk about angles between vectors that can span a full 360° because there is some natural orientation. As an example, for points on the unit sphere, we can assign unique angles over a span of 360° (the angle between a ray to that point and the x-axis) because we're oriented by the y-axis. If instead all we had was two rays with a common origin and nothing else to orient by, then we could only uniquely assign angles that span 180°.

Is there a common, succinct, and sensibly formal wording I can use to describe this distinction?

The best I can think of is to describe these angles as rotation angles (even if nothing is "moving").

  • $\begingroup$ Can you say "the angle in the counterclockwise direction"? $\endgroup$ – Rahul Dec 16 '16 at 8:56
  • $\begingroup$ @Rahul That works for the unit circle but I only meant that as an example. My intent was to ask for an abstract term. Roughly, I'm hoping to fill in something like "it's a __ type of angle so it spans _". $\endgroup$ – Praxeolitic Dec 16 '16 at 16:13
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    $\begingroup$ But to distinguish between a $90^\circ$ and a $270^\circ$ angle you always need a sense of clockwise/counterclockwise. That said, the obvious phrase "oriented angle" seems to have some degree of usage. $\endgroup$ – Rahul Dec 16 '16 at 16:27
  • $\begingroup$ @Rahul All I meant was that the specific phrase "(counter)clockwise" by itself won't always be clear. Maybe "oriented angle" it is then. $\endgroup$ – Praxeolitic Dec 16 '16 at 16:41
  • $\begingroup$ Nice pun, @Rahul $\endgroup$ – John Dvorak Dec 16 '16 at 22:01

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