Do any of you remember Jim Alison's Prehistoric Alignment Of World Wonders page, with his Great Circle that's shifted about thirty degrees from the equator? Let's look at it: if you grab the UVG-grid-compiled-by-B-Hagens.kmz file from Explore the UVG Grid with Google Earth, you'll see a Jim Alison Great Circle Projection optional line in there. If you turn off all the other Bethe Hagens lines and check the Jim Alison box, you'll see Jim Alison's Great Circle. Go to Google Earth to install Google Earth on desktop, and use KMZ files.

Now in 2019 though, I think it's time to be more precise with the calculations. We have to be more precise. In general, what geodetic system do you use for your calculations? I used WGS-84. Did you assume the world was a perfect sphere? In order to improve the calculations, I used the VBA functions from tdjastrzebski's Vincenty-Excel on GitHub. Using the VincentyInvFwdAzimuth function there gives a more precise bearing down to the meter, and doesn't assume the earth is a sphere. However, there are times when this VincentyInvFwdAzimuth does not converge, and gives a value of -1 in my case. If the value is -1 (which only happens rarely) then we'll have to rely on the old "posdist" function from geofunc.txt, where the distance is in nautical miles version (multiply by 1852 to get meters). We need both of these things because when you are finding distances all around the earth, you can't have ERROR or "DIDN'T CONVERGE" for an answer when you are trying to find the nearest two Great Circle points.

So what I did with that Vincenty-Excel function is combine it with my bearing/azimuth comparison VBA code in Microsoft Access. Instead of 62 points on a Bethe Hagens grid, I tweaked the bearing matching code to make it work with FOUR points (only one Jim Alison Great Circle line). It's faster if you hard-code the four Great Circle points in VBA code to compare bearings. Once you find the first (PT1) and second (PT2) closest Great Circle points, you compare the bearing or azimuth of PT1-to-PT2 with PT1-to-YOUR-POINT. If the bearing difference is +/- 0.25 like Jim Alison states, then it's "along the Great Circle line".

If you now revisit Jim Alison's points using Vincenty math, you'll see the actual bearing differences in his original locations (in the first link at the top). These points are actually NOT within a quarter of a degree of the Great Circle line:
Siwa: -0.812485276573909 deg. bearing diff.
Machupicchu: 0.651004475875226
Preah Vihear: -0.724089844901584
Khajuraho: -0.29734680561404
Mohenjo Daro: 0.919553790755756
Persepolis: -0.297160326312337

Petra: 0.811779844443663
Tassili n'Ajjer (actual): -0.643633448769037

Can anyone use Vincenty math and prove that Siwa is "within a quarter of a degree" of the Great Circle line? I don't see the result Jim does.

Jim's original listed coordinates for Tassili n'Ajjer appear to be wrong. Even if you use the actual coordinates for it of "25:48:48.9420 N, 08:08:01.8816 E", this spot is STILL not on the Great Circle line. Just Google "Tassili n'Ajjer coordinates" to see what I mean.

Wouldn't you then like to know EXACTLY what spots are within a quarter of a degree of Jim Alison's Great Circle line? I wondered too. So I used the allCountries.zip file from GeoNames Gazetteer: https://download.geonames.org/export/dump/"
This is A LOT I MEAN MUCHO rows for Access to handle. Due to memory issues and other "out of space" weirdness of Microsoft Access, you'll have to break up allCountries into 500,000 row text file bunches. Even then, you have to move one file at a time out to a copy of the database you're working with (a result database). If you don't keep track of the database size in Access you'll possibly corrupt your database.

But anyway, I did all this bearing/azimuth comparison for you and found 36,936 GeoNames points within a quarter of a degree of Jim Alison's Great Circle line.
Just download JimAlisonGreatCircleVerification.zip to use the same dbJimAlisonBlank.mdb I used in Access, and the list of 36,936 GeoNames points within a quarter of a degree. There are still lots of pyramids, tombs, and mosques along this Great Circle line. The first field in the list of 36936 points is in Unicode with the diacritics. The second field removes all the accents and is easier to search on. The third field are all the alternate names for the place, including their own Unicode characters that might be unreadable to you.
There are a lof of feature types in here, including cities, mosques, tombs, ancient sites, pyramids. Just look at the FeatureType field which comes from https://www.geonames.org/export/codes.html.

If you want to use dbJimAlisonBlank.mdb manually, yourself, that would be a rarity. In any case, you'll need to manually open the Immediate Window by pressing Ctrl+G, and typing "Call fClosest6JA("tblMyPoints")" (without the quotes). You can use any table with the fClosest6JA routine as long as you have the following fields:
Lat (Double type)
Lon (Double type)
PT1 (Text type, length at least 2)
PT2 (Text type, length at least 2)
PT1m (Double type)
AzimuthDiff (Double type)

By the way, PT1m tells you how close to PT1 your original point is. Using that logic, yeah there are some more points about 10,000 meters or less from a couple of the Great Circle points, but we were talking about a quarter of a degree in this verification.

The reason I'm asking for the Great Circle functions and geodetic system is because of this Fibonacci distance thing shown at www.human-resonance.org/phi.html". Are the points listed there actually accurate today if you google the coordinates?

Do you use Vincenty distances in meters in your calculations like I did? What's your function to find the distance of a circle on the earth? Does that function assume a perfect sphere, or are we not caring about the shape of the earth? Can I see the math to show how that point in Alaska of 59:42 N, 139:17 W is the center of that Great Circle? Can you show the math using online converters to show that the distance fromi Giza to that point in Alaska is actually 6219 miles? Because using any Geodetic system I can think of shows the distance being about 6229.99898184706 miles. Will the Fibonacci distance harmonics still work using Vincenty distances?

(To convert from meters to miles, multiply meters by .000621371192273338.)

Whenever anyone gives us a line around the earth, the default should be to show us the 36000 points along that Great Circle line within a quarter of a degree.

In summary, you can't just "zoom out real far" and say "hey wow this point is along the Great Circle line". I mean, we can't zoom out 50 miles above the earth. We have to use precise distances in meters and use azimuths in meters to prove a point is "within a quarter of a degree" of the Great Circle line.

If any of you care I did all this work, God bless you. You're a rarity.