Hello Sundial Listers,
I was wondering if anyone of us knew John B Mclemore, the Horologist
protagonist of the This American Life radio show S-Town. The story
includes his fascination with sundials and astrolabes. Was he known to any
of us?
-Bill
Of course, because only the four squared-terms are present, the two
binomials have to be chosen so that, when they're both squared, their
resulting middle terms cancel eachother out. (tan lat tan dec + 1) and (tan
lat - tan dec) meet that requirement.
Michael Ossipoff
On Mon, May 15, 2017 at 9:25
Wow. What can I say.
Your approach makes more sense in every way, than the way that I'd been
trying to find how the bead-setting procedure could have been arrived at.
I'd wanted to start with various pairs of points, and then find out if any
of them are separated by a distance of sec lat sec dec
Michael,
I seem to recall that sec^2(x)=1+tan^2(x)
Therefore sec^2(lat).sec^2(dec)=(1+tan^2(lat)).(1+tan^2(dec))
=1+tan^2(lat)+tan^2(dec)+tan^2(lat).tan^2(dec)
=(1+tan dec tan lat)^2 + (tan dec - tan lat)^2
I guess that this relationship, which is just a variant of sin^2+cos^2=1,
should have b
I asked:
"Or, I don't know, is that a trigonometric fact that would be already known
to someone who is really experienced in trig?"
Well, alternative expressions for the product of two cosines is something
that might be basic and frequently-occurring enough to be written down
somewhere, where som
Thanks for the Regiomontanus slide.
Then the original designer of that dial must have just checked out the
result of that way of setting the bead, by doing the calculation to find
out if
squrt((1+tan dec tan lat)^2 + (tan dec - tan lat)^2)) = sec lat sec dec, as
a trial-and error trial that?
Or,
