Editing Talk:2748: Radians Are Cursed
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::I mean, I'm sorry, but respectfully, you are wrong. The unit circle is *by definition* a circle of radius 1. There is no unit attached to that. [[Special:Contributions/172.71.82.41|172.71.82.41]] 01:55, 13 March 2023 (UTC) | ::I mean, I'm sorry, but respectfully, you are wrong. The unit circle is *by definition* a circle of radius 1. There is no unit attached to that. [[Special:Contributions/172.71.82.41|172.71.82.41]] 01:55, 13 March 2023 (UTC) | ||
:::Correction: The unit is that of the radius, ''by definition''. It is one of that unit, whatever that unit may be. You attach whatever unit you want to it, when you want to, but it isn't actually a unitless value when you start comparing it with othe values whose relationship and own unit are known. [[Special:Contributions/172.71.178.207|172.71.178.207]] 03:59, 13 March 2023 (UTC) | :::Correction: The unit is that of the radius, ''by definition''. It is one of that unit, whatever that unit may be. You attach whatever unit you want to it, when you want to, but it isn't actually a unitless value when you start comparing it with othe values whose relationship and own unit are known. [[Special:Contributions/172.71.178.207|172.71.178.207]] 03:59, 13 March 2023 (UTC) | ||
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There is actually some dispute about whether angles should be measured using units. I can't find it now, but there was an article by someone arguing that the current SI definition of the radian as 1 rad = 1 m / 1 m was flawed. He felt that units of angle should have a dimension, A, and rewrote several formulae slightly to accommodate this. But more often today, the radian is considered dimensionless with a value of exactly 1, making it not actually a "unit" so much as a hint telling how the angle was measured. In this definition, an angle has a measure of x (radians) iff the circular arc it intercepts as a central angle has an arclength of x times the circle's radius. Under this definition, the following become mathematically correct: | There is actually some dispute about whether angles should be measured using units. I can't find it now, but there was an article by someone arguing that the current SI definition of the radian as 1 rad = 1 m / 1 m was flawed. He felt that units of angle should have a dimension, A, and rewrote several formulae slightly to accommodate this. But more often today, the radian is considered dimensionless with a value of exactly 1, making it not actually a "unit" so much as a hint telling how the angle was measured. In this definition, an angle has a measure of x (radians) iff the circular arc it intercepts as a central angle has an arclength of x times the circle's radius. Under this definition, the following become mathematically correct: | ||
