I'm dealing with something that is equivalent to the logarithm, sure. But since I'm not using anything beyond real numbers, this is infinitely simpler than bive

I'm dealing with something that is equivalent to the logarithm, sure. But since I'm not using anything beyond real numbers, this is infinitely simpler than bivectors or complex logarithms and I don't need calculus. The rational angles are only used to introduce the trigonometric functions. From then on we can deal with any real angle using arcs of circles and trigonometric functions. Therefore we don't have any issues. We can deal with angles perfectly well as long as we can know the circumference of a circle. Whereas otherwise we would need either calculus or complex numbers, but we need geometry to make sense of them and we need angles to make sense of geometry without handwaving or making it needlessly difficult to learn. In other words, an angle measure isn't a logarithm, a logarithm is equivalent to an angle measure when we accept constructs that are not necessary but are sufficient to angle measures.