No, they were just used mainly for navigation. The reason why the Mercator projection was popular for so long is that its angles correspond to compass points and you navigate by a trivial algorithm:

1. Draw a line to your destination on the map and determine its angle with the north, say 25 degrees north-east.

2. Set your course at 25 degrees north-east and keep it constant. Your will arrive to your destination by a rhumb line [1], which is only slightly less efficient than a great circle.

[1] http://en.wikipedia.org/wiki/Rhumb_line

Mercator preserves shape and direction at the expense of size. Peters preserves size and direction at the expense of shape. Peirce Quincuncial preserves shape and size at the expense of direction. Here's a transverse Peirce Quincuncial map I generated: http://frammish.org/tpq.jpg

Many other projections try to combine these, like the Miller projection maintains direction but strikes a balance between shape and size, getting neither one right, but neither is horribly wrong either. The Winkel Tripel projection tries to balance all three attributes.

I wonder if there is some sort of theorem that describes which fidelities you can get out of a flat projection of the surface of a sphere. For example, a projection could have accurate area ratios or accurately reflect point to point distances but not both.

I'm not sure any of this is really accurate. Go read the wikipedia page: http://en.wikipedia.org/wiki/Gall%E2%80%93Peters_projection#...

tl;dr:

-Peters wasn't novel. An identical projection was created a century earlier (that's why it's called Gall-Peters).

-Peters made completely BS claims about his projection.

-Cartographers had already been using plenty of projections beyond Mercator for a long time and they knew very well that it had problems.

By the way, I'm pretty sure the xkcd about projections has a punchline and hover text that is directly related to the information above.

http://en.wikipedia.org/wiki/Dymaxion_map

If you are interested in a size-accurate map, you can't get much better than that.

CE sucks.

http://calabarboy.com/2010/10/11/the-true-size-of-africa-kai...

Personally I'd prefer a map that emphasizes that the world is actually a sphere, rather than a rectangle. I also have a soft spot for Dymaxion, although I don't use Dvorak.

I might take up the project of posting the relevant wikipedia links as stories, and in turn linking those in the comments of all shoddily written blog posts, in the hope of righting these wrongs.

But this whole "true size" is true in measure, but I'm not really comfortable with people using it to push their agenda

Yes, Africa is big, and?

Big countries (yes, Africa is not a country) are usually on the wrong side of the stick. Maybe the USA has the most usable land, but it's still costly for them

Asia is gigantic, where's its population? Concentrated into tiny spaces! Japan, Indonesia, a narrow stretch of India.

Obviously not the best for navigation, but considered the best compromise for viewing the entire Earth in two dimensions.

[1] http://en.wikipedia.org/wiki/Robinson_projection

Personally I really like this one: https://en.wikipedia.org/wiki/Dymaxion_map It's basically a net that you can print of and fold together.

It means that geographically, Kazakhstan is the 9th largest country in the world. And not much else.

I did not like the picture showing various countries contained within Africa. Why is Alaska not considered part of the "US"?

Several times while driving North through mid-western States I've been startled to realize how much land is north of the US border in Canada. I knew Canada was larger than the US, but I didn't comprehend the scale of that country.

I knew college professors who believed that most map projections have a eurocentric bias, but it makes almost as much sense that creating maps and globes is easier to do if you assume the Earth is a perfect sphere.

I've always wondered, however; why not increase the density of faces (or vertices?) from an icosahedron, and have an even less distorted map? What would the monstrosity look like?...