[hervature]

Radians vs. degrees isn't notation, it's a convention. You even say the reason why it is the convention. That multiplying the radius by the radians gives you the circumference. It is the only representation of angles with this special property. I mean, why should 360 represent 1 rotation? Why not use rotations itself? That way 1/4 is 1/4, 1/8 is 1/8, and so forth.

[redsaz]

Using rotations is exactly what the poster proposed:

> I think that the most sensible universal angle unit is "rotations". So, 360 degrees is 1, 45 degrees is 1/8, and so forth.

It was a bit confusing because most of the post was about radians, then switched to degrees. It could have instead read:

> 2pi radians becomes 1 rotation. pi radians becomes 1/2 rotations. pi/2 becomes 1/4 rotations.