Eisenlohr’s optimal conformal map of the world

[Atarimaster]

Of course, I find it right after I post. At least, I think this is it

Yes, that is a correction.

btw, the link you posted doesn’t work for me, I get an error 404.
I hope this one works.

[daan]

Hm. I think I mangled the link when copying it. Thanks for fixing that and for confirming the site of the correction, Tobias.

Cheers,
— daan

[mapnerd2022]

Thank YOU, Mr Strebe for all the interesting info about the Eisenlohr Epicycloidal and the August!

[daan]

Thank YOU, Mr Strebe for all the interesting info about the Eisenlohr Epicycloidal and the August!

Couldn’t do it without my friends.

— daan

[mapnerd2022]

Yeah, friends are great indeed!

[mapnerd2022]

And so is this forum!

[mapnerd2022]

On a related note: There's a paper called «World maps on the August epicycloidal» by Erwin Schmid of the NOAA which used to be called the US Geodetic and Coast Survey, as well as US Survey of the Coast.

[daan]

On a related note: There's a paper called «World maps on the August epicycloidal» by Erwin Schmid of the NOAA which used to be called the US Geodetic and Coast Survey, as well as US Survey of the Coast.

I have that pamphlet. It’s odd that NOAA devoted the time to put that out. As Milo points out here, the August is an arbitrary function, so why would you use it if you could use Lagrange, which meets an optimality criterion? If you parameterize Lagrange such that it has the same width as August and the same scale at the center, then the Lagrange looks similar but has less area than the August. That means that, on average, points have less areal inflation.

Cheers,
— daan

[mapnerd2022]

I didn't know that! Thank you for the interesting explanation!

[Milo]

As Milo points out here, the August is an arbitrary function, so why would you use it if you could use Lagrange, which meets an optimality criterion?

As far as I know, the optimality of the Lagrange projection was only noticed in this forum. It was first suggested for this purpose by dummy_index, then expanded on by me, but still without a formally-rigorous proof (even though I'm satisfied by it).

So most likely, it just didn't occur to them to try the Lagrange projection.