Turns are better than radians
>But math never decreed that sine and cosine have to take radian arguments!<p>Ummm, actually it did. The Taylor-series of sine and cosine is the simplest when they work with radians. Euler's formula (e^ix = cosx + isinx) is the simplest when working with radians.<p>Of course you can work in other units, but you'll need to insert the appropriate scaling factors all over the place.<p>"Turns" don't generalize to higher dimensions either. With radians you can calculate arc length on a circle by multiplying with the radius. This extends naturally to higher dimensions: a solid angle measured in steradians lets you calculate surface area on a sphere by multiplying with the radius. How do you do the same with "turns" on a sphere? You can't in any meaningful way.