Eisenlohr’s optimal conformal map of the world

[quadibloc]

Your "mess" is the evaluation of an indefinite integral, yet in the previous post where you referred to the evaluation of an integral being a mess, the integral was this definite integral:

equation.jpg (8.03 KiB) Viewed 8773 times

[daan]

It is sometimes possible to find a closed-form solution to a definite integral without knowing a closed-form solution to the indefinite integral. I’m no good at that, though, and Maple certainly doesn’t know the solution to either situation here. Knowing a closed-form for the indefinite integral generally yields a closed form for the definite integral, of course.

But maybe I’m missing what you’re getting at.

— daan

[daan]

You're one of the people who got me so interested in and knowledgeable about map projections! I have read your map projections papers a lot, they're really interesting, intriguing and of course what is written on them is really incredible! Like Mr.Jung, I'm not not just any layman; I DO care about map projections and find them interesting and even fun to mess with. You won't believe me when I say I saw a Mercator projection having been used to show the worldwide distribution of covid19 cases and that I also saw it on TV being used in one Portuguese school(an elementary school, no less!) ( Particularly when children believe anything they see, even a nightmare-ish, unbalanced and greatly distorted representation of the world and especially of the polar regions) that has taken in/integrated some chilidren from Ukraine. It's really sad how they don't just have someone with some map projection expertise choose a more balanced and pleasant view of the world such as the Robinson or the Winkel Tripel in either the original, the Bartholomew or the Oxford versions. Sigh...

Many thanks for the kind words.

I would not be surprised by any deployment of an inappropriate projection anymore. I wish people would rely more on experts—regardless of domain.

— daan

[mapnerd2022]

Yes, you're absolutely right. But it still makes my skin crawl.

[Milo]

I wish people would rely more on experts—regardless of domain.

I respect people who seek to understand something on their own more than those who blindly follow the advice of someone who claims to be an expert.

I don't think I count as an "expert" on the field of map projections. I have no formal education in the subject and have not held any professional employment in the field. But I've read up about them because I find them interesting, and I'd consider myself to be fairly knowledgable now (I even recently invented a cool projection of my own). I don't even remember what originally got me into the subject, but it was probably something along the lines of "I wonder what would be the best map projection to use for such-and-such application". That's just the logical question to ask for anyone who wants to make a map and is aware that there exists more than one map projection in the universe.

If you can't understand basic concepts like "some map projections preserve angles but distort areas while other map projections preserve areas but distort angles" on your own, you have no business publishing any maps at all, even in a projection that someone else recommended to you.

[mapnerd2022]

We're in the 21st century, for God's sake! I thought misuse of the Mercator would stop at the 19th century. It was at that century that at least some atlases were using, for example, the Hammer projection witch is much better for a general use world map.

[Atarimaster]

We're in the 21st century, for God's sake! I thought misuse of the Mercator would stop at the 19th century. It was at that century that at least some atlases were using, for example, the Hammer projection witch is much better for a general use world map.

Well, I don’t think I have ever seen the Mercator projection in an atlas printed in 1970 or later (speaking of german atlases, which are the only ones of which I have seen several).

However, it can often be seen in newspapers etc. – and yes, mostly inappropriately.

[mapnerd2022]

The newspaper part doesn't surprise me much. I think the quality of journalism and journalists is decaying, at least here in Portugal. I mean, even when it comes to the Portuguese grammar rules, they make rookie mistakes and even outrageous ones. It's like they don't know how to speak Portuguese even though they're obviously from Portugal.

[Milo]

I think part of the problem is that the Mercator projection has a reputation of being "the map used by professionals", due to having properties that are valuable for navigators, the one profession where being able to accurately read maps is an important part of the job (or was, before the advent of computers that can easily calculate courses from the coordinates alone without needing a physical map). What this is overlooking is that it's a specialized map projection that's useful only for a niche role that only a minority of people in a very specific profession care about, and is poorly-suited for typical uses of maps by laymen or even professionals in other fields.

Meanwhile the plate carree projection is actually a pretty good projection, as cylindrical projections go, but its extreme simplicity gives it a reputation as a naive map projection used by amateurs who don't know what they're doing, because people just can't believe that something that obvious could be "professional".

Which, again, shows the dangers of blindly following "experts" without checking what they're experts in.

[mapnerd2022]

I absolutely agree.