2 ms·
A radian is 1turn/2pi. It is not dimensionless. A radian, or a turn, has a dimension: angle. Saying 1radian=1 is just as senseless as saying 1m=1=$1. It's t
by lupire 4y ago
A radian is 1turn/2pi.
It is not dimensionless.
A radian, or a turn, has a dimension: angle.
Saying 1radian=1 is just as senseless as saying 1m=1=$1.
It's true that abstract math often drops units because some things (like Taylor series) work nicely in certain units. That doesn't make the unit meaningless.
Street-Fighting Mathematics, thesis/book by Sanjoy Mahajan, shows what amazing things you can die in abstract math if you don't forget units.
- bmacho 4y agoIt is de juro dimensionless, SI said so, and your government most likely made it official. https://en.wikipedia.org/wiki/Radian#Dimensional_analysis https://en.wikipedia.org/wiki/Radian#Dimensional_analysis https://en.wikipedia.org/wiki/Radian#As_a_SI_unit https://en.wikipedia.org/wiki/Radian#As_a_SI_unit I am not sure that the current definitions are consistent or useful, but I myself don't know better.
- panda-giddiness 4y agoSorry, but this is incorrect. An angle is defined through the ratio of two objects with common units; it is dimensionless for the same reason that 5m / 5m is dimensionless. You could argue that radians should only refer specifically to angles, but your own example demonstrates how impracticable that would be: you can't sensibly Taylor expand a trigonometric function (eg, sin(x) ~ x) if the left-hand side and right-hand side have incompatible units.