A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Lars Bergman
Date: 2018 Nov 11, 13:58 -0800
Frank, you wrote: "Angle is "size divided by distance". In succinct terms: θ = s/r. That relationship doesn't "calculate" the angle theta; it defines its meaning. Every angle is a ratio -- just a number. It has no units, no dimensions."
Size must have some dimension, as have distance. Let's say we use meters. Divide meter by meter. This equals one. So the dimension is one. I am fully aware that "dimensionless" (dimension = 0 ??) is often used for this case, but a more correct expression is dimension = 1.
Further, you wrote: "Radians are not anything at all except a name to tag on the end to avoid confusing readers without basic math insights."
Radian is an "SI derived unit" for plane angle, so you should not discard it that easy. According to SI it has dimension = m/m = 1.
But this discussion is somewhat off topic, owing to you I have realized how to pre-calculate the rate of change of the apparent lunar distance, where it all started! Thanks.