Don,
I think the problem becomes understandable after your observation about the circumference becoming smaller as you go towards the center. Coupling this understanding with the concept of thinking of the turning as a solid cylinder reduces everything to relatively straight-forward geometry and trig.
The crux of the issue lies in the reduced circumference of the inside of the turning relative to the outside. Because of this something has to change between the two surfaces.
In a “perfect” world the outside of the cut would be at 90deg, and the inside of the cut would be at a smaller angle depending on the thickness of the turning. This would allow the depth of the V to remain constant, and keep the arc of the circumference it removed constant. Given we don’t have a “modulating angle” router bit, it will *always* cut 90deg; therefore we have to compromise something.
By canting the angle of the router track the compromise we choose is to modulate is to reduce the depth of the V, this allows the arc it removes to still be the same proportion of the 360deg circumference. This will raise a square shaft of wood slightly on the inside and two adjacent pieces will need to be trimmed (towards the inside) to provide a perfect fit.
Again, fortunately, wood is a forgiving medium so we can get away splitting the difference, or other inexactitudes.
If you draw the angles out recognizing that all radial lines come to a point at the center of the cylinder, and remember a little trig (opposite/side of a triangle = tangent) you can compute finer angles than the wood will care about.
Thanks for motivating me to think of schooling from 40yrs ago