Most widely used projections

[Atarimaster]

I’d add Goode homolosine to your list – I don’t think that it is used very often, but IF there’s an “interrupted” world map, it’s always this one.

I stand corrected.
I do have an atlas that uses an interrupted population density map. I don’t know why – as mentioned above, a density map should always be equivalent, but since most other thematic maps in that atlas are Wagner VII, that can’t be the reason. I would suspect that the maps is using McBryde’s continental interruption scheme, applied to the Mollweide projection, with the atlantic cut running along 20°W – but the map is truncated and partially overlaid but the legend, so it’s hard to say.

There are also two maps (showing volcanic activity and earthquakes) using an oceanic interruption scheme that I haven’t seen before, definitely not Goode’s or McBryde’s.

[daan]

PeteD,

Is your inquiry about contemporary maps? Or, how far back in time are you willing to consider?

— daan

[PeteD]

Contemporary maps.

[PeteD]

Yes, but David Alexandrovitch Aitoff moved to France at the age of 23, and remained there for the rest of his life.

Is he the same David Alexandrovitch Aitoff who was the father of Vladimir Aïtoff and Irène Aïtoff?

Is Aitoff/Aïtoff a French transliteration of name, while Aitov/Aitow is a direct transliteration? How does he spell it in his French atlas?

[Atarimaster]

Is Aitoff/Aïtoff a French transliteration of name, while Aitov/Aitow is a direct transliteration?

Both Winkel and Wagner wrote Aïtoff so I doubt this is a French (-only) transliteration. One of them (I think it was Winkel but I’d have to check) pointed out somewhere that the spelling Aitow should not be used, most likely to avoid confusion with eastern Germany names ending with -ow (the w is silent there).

[PeteD]

One of them (I think it was Winkel but I’d have to check) pointed out somewhere that the spelling Aitow should not be used, most likely to avoid confusion with eastern Germany names ending with -ow (the w is silent there).

Could it instead be that he pointed it out because many readers might naturally assume an -ow ending since this is common for German transliterations of Russian names, e.g. Romanow, Tschechow, Pawlow, Chruschtschow, Gorbatschow (English: Romanov, Chekhov, Pavlov, Khrushchev, Gorbachev)? In contrast, I can't think of any other Russian names transliterated with an -off ending.

[quadibloc]

Many Russian names end in what is now translated as -ov, since that suffix means "son" in a family name. But in Russian, the final letter "v" is pronounced as "f" - well, at least, if it's not palatalized. Since, in English, a single "f" at the end of the word, as in the word "of", is usually pronounced as v, it's necessary to double the f in order to ensure that the name is pronounced correctly.
It's a cultural change - it used to be that foreign names were transcribed in English according to their pronounciation, but now the approved approach is to apply the current official transliteration scheme to the language instead.

[PeteD]

So I've been getting the pronunciation of those names wrong for all these years!

What about the diaeresis over the I? Does that come from the French transliteration? I don't know anything about Russian, but I always assumed the correct pronunciation was "eye-toff". Is that right? If so, there's no way of writing that exactly in French, but "Aïtoff", where the "aï " would be pronounced as in "naïve", would be closer than "Aitoff", which would be pronounced more like "ettoff".

[Milo]

Hmmm.
I’ve seen Gall-Peters a couple of times, even outside of cartography discussions (probably no other cylindrical equal-area projections). But I don’t remember to have seen equirectangular maps in actual use (i.e. other than being a resource for map makers).
Maybe I have seen some of them, especially on websites, but I don’t remember it.

I guess this highlights the need for actual studies rather than "I think I've seen this somewhere".

I know that one website that I actually use from time to time, Great Circle Mapper (great for measuring distances between places and seeing what the paths look like), offers a choice of three projections: plate carree, orthographic (polar or oblique), or azimuthal equidistant (always oblique). Notably, its implementation of the equirectangular projection is rather poor, as even when mapping a small region, it's always plate carree, instead of shifting the standard parallel into the relevant region. (Usually I use it with whole-world maps or regions large enough that it doesn't matter.)

On Wikipedia, the plate carree is used for the world-by-meridian-or-parallel navigator, although here there's an actual strong reason to favor it over all other projections, rather than just using it as a compromise projection.

That's just what I can think of on short notice.

But you're probably right that Gall-Peters gets used more often than I gave it credit for, too. I figured that since its supporters mostly advocate it as an alternative to the Mercator projection, it wouldn't really appeal to people unless they were previously either using the Mercator projection, or didn't know any map projections at all. But then I guess such people do exist.

Well, for "thing-per-area metrics", equal-area projections should be used but aren't always,

There will always be idiots.

If the data shown isn't a "thing-per-area metric", then I don't see any particular reason to use an equal-area projection.

Well, it would still be helpful in showing how relatively common the high/low ends of the metric you're measuring are. Like, temperature isn't a thing-per-area metric (in the sense that a 200-square-kilometer area isn't twice as hot as a 100-square-kilometer area, although you might argue it does have twice as much heat energy...), but it can still be useful to know whether it's better to think of Earth as mostly warm with some cold spots, or mostly cold with some warm spots. (I would expect mostly warm with some cold spots, since 50% of Earth's surface is within 30° of the equator, although comparatively less of the land is.)

Yes, it isn't as important as when measuring thing-per-area metrics, but it's still valuable.

Of course, then you get to thing-per-capita metrics, where it might be useful to use a cartogram instead of a normal map projection...

I've seen at least one case of an article using Mollweide, apparently as a scientific-community-accepted "default" map projection, in the one context that I really wouldn't recommend its use for: a climate simulation of weather on a tidally-locked planet, where, of course, the effect of latitude relative to the equator is far less dominant than on normal planets!

What would you have used? A two-hemisphere projection?

Probably. Either that, or just a single azimuthal projection centered on the substellar point, depending on whether I prioritized reducing distortion or keeping the map uninterrupted.

(Note that Mollweide can technically be used to make a two-hemisphere projection too - they'll even look circular! - but that obviously isn't what we're talking about here.)

[Atarimaster]

Could it instead be that he pointed it out because many readers might naturally assume an -ow ending since this is common for German transliterations of Russian names, e.g. Romanow, Tschechow, Pawlow, Chruschtschow, Gorbatschow (English: Romanov, Chekhov, Pavlov, Khrushchev, Gorbachev)? In contrast, I can't think of any other Russian names transliterated with an -off ending.

What I meant was that Winkel might have rejected the -ow transliteration in general, because of East German names like Teltow, Pankow, Kleinmachnow, von Schlütow etc. in which the w is silent. Someone familiar with these names might say “Aito, Romano, Pawlo” etc. and therefore, Winkel preferred Aïtoff. Of course I’m speculating here, I only know for sure that he explicitly rejected the spelling “Aitow” – I’ve found it now, it’s in “Die azimutalischen Erdkartenentwürfe von D. Aïtoff und E. v. Hammer”, published in: Geographische Zeitschrift, edited by Dr Alfred Hettner, 1922.

What about the diaeresis over the I? Does that come from the French transliteration? I don't know anything about Russian, but I always assumed the correct pronunciation was "eye-toff". Is that right?

I guess the correct spelling is “ah-eetoff” – that’s what the diaeresis suggests in German, and Winkel must have suggested this spelling for a reason. Eckert in 1906 and Zöppritz/Bludau in 1912 who wrote “Aitow”. Even if the diaeresis originates in the french transliteration, I doubt that Winkel would have used it if the correct pronunciation was "eye-toff".