Most widely used projections

[daan]

Aitoff-Hammer projection of the sphere is far more often used than the Mollweide for mapping the celestial sphere. For the cosmic microwave background and other purposes.

I’m not sure about this. Mollweide is often used for visualizations of the microwave anisotropy results, as well as for any other cosmological studies that I’ve seen portrayed on oval projections over the years. (The quadrilateralized spherical cube was designed for COBE visualizations, but rarely seen.) Often, the projection is not declared in cosmological visualizations, making it practically impossible to tell, but when it is declared, the examples I have seen have always been Mollweide. I don’t recall ever seeing astronomical use of the Hammer outside of “the celestial sphere”, as in some star maps for astronomy, rather than cosmology. Professor Mollweide himself was an astronomer, used the projection for celestial maps, and inspired its use in the field. Mollweide examples:

• COBE DMR 2 & 4 Year Images
• COBE Slide Set, slide 8
• Wilkinson Microwave Anisotropy Probe
• Ask Ethan: Why Are Maps Of The Cosmos Oval-Shaped?
• PLANCK SKY COVERAGE - MOLLWEIDE PROJECTION
• Why are maps of the universe elliptical?

Cheers,
— daan

[Milo]

So recently I stumbled across a site that shows what appears to be an equirectangular projection, but claims it's a Mercator projection.
http://www.euclideanspace.com/maths/geometry/rotations/euler/singularity/index.htm (link is actually to Wayback Machine in case this ever gets fixed)

You can easily tell by the shape and size of Greenland that this can't be the real Mercator projection, and also the claim that "the Mercator Projection maps the north and south poles to lines" is patently wrong (most cylindrical projections do, but the Mercator projection doesn't because it pushes the poles to infinity).

Well, the footer does say "This site may have errors. Don't use for critical systems.".

[daan]

So recently I stumbled across a site that shows what appears to be an equirectangular projection, but claims it's a Mercator projection.
http://www.euclideanspace.com/maths/geometry/rotations/euler/singularity/index.htm (link is actually to Wayback Machine in case this ever gets fixed)

Startling for a site with a mathematical bent!

Original link shows as live for me. You might try it as https instead of http.

— daan

[quadibloc]

But I don’t remember to have seen equirectangular maps in actual use (i.e. other than being a resource for map makers).

I have seen equirectangular maps in actual use... in one place. But not in atlases.
In NASA technical publications, where the orbits of satellites or spacecraft are charted.

[Milo]

But I don’t remember to have seen equirectangular maps in actual use (i.e. other than being a resource for map makers).

I have seen equirectangular maps in actual use... in one place. But not in atlases.
In NASA technical publications, where the orbits of satellites or spacecraft are charted.

Are you sure those were equirectangular?

If the orbits looked like straight lines, then it's actually a specialized "satellite-track projection", by Snyder.

[quadibloc]

I don’t recall ever seeing astronomical use of the Hammer outside of “the celestial sphere”, as in some star maps for astronomy, rather than cosmology.

It is true that one famous astronomical use of the Hammer is the painting created by the Lund Observatory.
But I remember seeing the Hammer quite frequently in charts of the sky in articles in Scientific American from the 1960s onwards.
Searching on the Web, many maps don't have graticules, so whether they're Mollweide or Hammer is hard to tell. I've found a few examples of Hammer:
https://aether.lbl.gov/www/projects/neu ... UTION.html
https://imagine.gsfc.nasa.gov/news/02dec96.html
http://dfa.ua.es/~ignacio/xbin.html
https://phys.org/news/2013-12-swift-sat ... x-ray.html

[daan]

But I don’t remember to have seen equirectangular maps in actual use (i.e. other than being a resource for map makers).

Sadly, plate carrée maps infect thousands of scientific papers, as well as the map used for civil and environmental engineering projects and studies. It’s the default projection for Esri’s ArcGIS and other GIS products. Knowing nothing about projections, the authors didn’t change the default. It’s not uncommon to see even regional or local maps with the ugly, deceptive horizontal stretching characteristic of mid and higher latitudes on that projection.

And, more shockingly, the spatial analysis is often performed in projected space… and thus is wrong.

Cartography and GIS are distinct fields. Often there isn’t any cartography going on in GIS beyond the defaults from the software.

— daan

[mapnerd2022]

Yes, because it's the simplest projection of all, and of course due to the rectangular outline fitting the page rather easily.

[daan]

It is true that one famous astronomical use of the Hammer is the painting created by the Lund Observatory.
But I remember seeing the Hammer quite frequently in charts of the sky in articles in Scientific American from the 1960s onwards.
Searching on the Web, many maps don't have graticules, so whether they're Mollweide or Hammer is hard to tell. I've found a few examples of Hammer:
https://aether.lbl.gov/www/projects/neu ... UTION.html
https://imagine.gsfc.nasa.gov/news/02dec96.html
http://dfa.ua.es/~ignacio/xbin.html
https://phys.org/news/2013-12-swift-sat ... x-ray.html

Thanks for tracking those down! It looks like the field of high-energy EM exploration has a convention of Hammer maps. Specialties often go separate ways.
¯\_(ツ)_/¯

— daan

[quadibloc]

It’s not uncommon to see even regional or local maps with the ugly, deceptive horizontal stretching characteristic of mid and higher latitudes on that projection.

If they adjusted the projection to the latitude, plate carree would be just fine for small-scale maps. If they can't be bothered to do that, then they should step up to Mercator. Which is, of course, basically the reason why Google Maps uses Mercator. Some have criticized their decision, but I think it shows they were thinking clearly - making it as simple as possible, but not even simpler, so that things go wrong, as the saying goes.