Eckert IV vs Eckert VI. Other related topics.

[RogerOwens]

By the way, it occurs to me that there's a good justification for calling cylindrical projections "pseudocylindrical", because cylindrical is just an extreme special case of pseudocylindrical. Still, I like using them with mutually-exclusive meanings, because then it's only necessary to say "pseudocylindrical", to denote that I'm not talking about a cylindrical.

So I like to say "cylindroid" when speaking of them both collectively.

A few moderations of positions I've taken:

Linearity isn't necessary for easy position-measurement, if you provide a latitude-ruler, and the map is cylindroid. Then, with a pseudocylindrical or cylindrical, you can have both equal-area and easy position measurement. ...or, with a Cylindrical-Conformal, you can have conformality and easy position-measurement.

I used to say that equal-area is only needed for special purposes, like some kinds of thematic maps. But more recently it occurs to me that equal-area, by dividing a map's area equally according to the area of geographical regions, gives fairness to people who want to look at various different regions. ...regardless of the map's purpose.

(...but of course not helpful if the purpose is navigation)

While it's true that Mercator doesn't shrink Ecuador to magnify Greenland, it's also true that a large map could share its larger area equally according to regions' areas, in fairness to people interested in different places.

But, while a little bit of scale-disproportion is ok, to achieve equal-area with large space-efficiency, I don't think someone who wants to study equatorial places would want them magnified by means of a 2:1 scale-disproportion, which they have when CEA is conformal at lat 45.

Michael Ossipoff