3 ms·

Calculations are so much easier when it's a unit circle/sphere. Here's my favorite trick: the radians of an angle in a unit circle is equal to the length of th

Calculations are so much easier when it's a unit circle/sphere. Here's my favorite trick: the radians of an angle in a unit circle is equal to the length of the arc of that unit circle.

baggy_trough 6y ago
That's not exactly a trick. It's the point of the definition.
- saeranv 6y ago
  I think you're being needlessly pedantic. Just because it's easy to derive doesn't mean it's immediately obvious. I only realized it when I watched a 3Brown1Blue video where he pointed it out as interesting property of the unit circle. That alone tells me its not that obvious to many.
  - srean 6y ago
    You did not get parents comment. Its not a derivation its a definition.
    - saeranv 6y ago
      Personally, that again sounds like a very pedantic and obvious point to me. However, I could be wrong so feel free to break down your point further. My interpretation is that I think you guys are missing the fact that the intent of my original comment is in the context approximations, from which you can see the use of the 'trick' is correct. To break it down a little further: the trick I am referring to is in practice it's often convenient to scale approximations so that you can use the unit circle for calculations, since you can use the radians as a measurement of arc length. If it's not a unit circle, the angle != arc length, so that convenience is lost.
      - srean 6y ago
        > Just because it's easy to derive doesn't mean it's immediately obvious is what I was responding to. My point is this -- there is no derivation happening there. If it was pedantic, obvious and simple to you as you claim, I wonder why you claimed that it was a derivation. To you the distinction between a definition and a derivation might be a pedantic one, I have doubts on whether that is an universal or even an useful position to have.

3 ms·

Calculations are so much easier when it's a unit circle/sphere. Here's my favorite trick: the radians of an angle in a unit circle is equal to the length of th

by saeranv 6y ago

Calculations are so much easier when it's a unit circle/sphere. Here's my favorite trick: the radians of an angle in a unit circle is equal to the length of the arc of that unit circle.

baggy_trough 6y ago
That's not exactly a trick. It's the point of the definition.
- saeranv 6y ago
  I think you're being needlessly pedantic. Just because it's easy to derive doesn't mean it's immediately obvious. I only realized it when I watched a 3Brown1Blue video where he pointed it out as interesting property of the unit circle. That alone tells me its not that obvious to many.
  - srean 6y ago
    You did not get parents comment. Its not a derivation its a definition.
    - saeranv 6y ago
      Personally, that again sounds like a very pedantic and obvious point to me. However, I could be wrong so feel free to break down your point further. My interpretation is that I think you guys are missing the fact that the intent of my original comment is in the context approximations, from which you can see the use of the 'trick' is correct. To break it down a little further: the trick I am referring to is in practice it's often convenient to scale approximations so that you can use the unit circle for calculations, since you can use the radians as a measurement of arc length. If it's not a unit circle, the angle != arc length, so that convenience is lost.
      - srean 6y ago
        > Just because it's easy to derive doesn't mean it's immediately obvious is what I was responding to. My point is this -- there is no derivation happening there. If it was pedantic, obvious and simple to you as you claim, I wonder why you claimed that it was a derivation. To you the distinction between a definition and a derivation might be a pedantic one, I have doubts on whether that is an universal or even an useful position to have.