When I listed trig, in my previous message, I was referring to the fact that there's a 3rd derivation-approach that applies plane trig at the dial itself (but of course not just on the horizontal-plane).
With any one of those 3 derivation-approaches, it would be necessary to explain either some 3-dimensional analytic-geometry; or the derivation of at least the formula for altitude (or maybe azimuth too) from h and dec; or trig for the solving of triangles. The trig needed for deriving the altitude and azimuth formulas consists only of direct use of the definitions of the trig functions, whereas the trig-at-the-dial derivation involves several plane triangles, and the solution of a non-right triangle...meaning that the person you're explaining to would have to hear about more trig than that required for deriving the altitude-formula. The altitude and azimuth formulas can be directly and straighforwardly derived by applying the definitions of the trig functions to an orrery. ...for a brief and straightforward derivation that would make sense to anyone with no prior experience in the subject. On Sun, Nov 17, 2019 at 1:42 PM Michael Ossipoff <email9648...@gmail.com> wrote: > I mean, when you're choosing which declination-lines > construction-explanation to use, there's the matter of: Which of the > following is that person more likely to have occasion to use? Or which is > more likely to be of interest and use to someone interested in sundials or > astonomical matters?: > > Altitudes (or terrestrial distances) and azimuths? > > 3-dimensional analytic geometry > > trig > > 3-dimensional analytic geometry and trig are of course useful for many > things. But celestial altitudes and azimuths, and terrestrial distances, > are of frequent and direct use and interest to people interested in > sundials or astronomical matters. > > So that's why I'd give the altitude &/or azimuth explanation for > declination-line construction. > >
--------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
