Rectangular maps result from Cylindrical projections, of which there are several. The the square grid and you dropped on the second map, and the 2:1 aspect ratio, would make it "Plate Carree" which is a special case of the "Equidistant Cylindrical" or "Equirectangular" projection which is often used for raw data, but doesn't make for very good finished maps because it significantly distorts both angles and areas, and that distortion is rather ugly looking.Originally Posted by BookOwl
Really, projections are something you need to think about before you start drawing the map. They ALL cause some form of distortion and you have to understand that distortion and draw it into the map, otherwise what you've done is distorted the features themselves in order to compensate.
Think about what it means to put a globe on a rectangle. In your case, the equator and lines running straight north-south are "true" but other lines are distorted. If you walk along the 45th parallel on a globe, it will be about 70% of the length of the equator, but on your map, it's exactly the same length. The 75th parallel is only 25% as long as the equator, and at the poles, you have single points without length, but on your map they are infinitely stretched out to become lines as long as the equator. So as you get closer to the poles, everything gets stretched out east-west on a cylindrical map. Equidistant Cylindrical leaves north-south distance alone, so shapes on the map should be progressively more and more stretched out sideways as you near the poles. If they shapes aren't stretched on the map, then it means that the the real shapes are "pinched" in toward the poles.
Other projections try to compensate. Mercator adds a north-south stretch equal to the east-west stretch, which keeps shapes/angles correct. It also drastically distorts areas, and pushes the infinitely stretched poles infinitely far away. It was created for marine navigation as it preserves compass bearings, which makes it the only projection where you can have a whole world, and put a compass rose on it (compass roses are not decorative, they are there to indicate that the map preserves bearings)
The other main cylindrical projection is the Equal Area Cylindrical projection which does the opposite of Mercator, squashing north-south where it stretched east-west so it balances out and keeps the area the same, but distorts the shape even more. Gall-Peters and Hobo-Dyer are both particular cases of this projection. It's ugly, hard to read, and generally no good far anything. There are non-cylindrical Equal Area projections that are far superior like Mollweide and Aittoff. Equal area maps are generally used for thematic maps that display data like population or weather, not for reference or navigation maps.
There are loads of other non-cylindrical projections including Azimuthal, Conic, Pseudocylindrical, and Hybrid projections. Modern world maps tend to use Hybrid projections like Robinson and Winkel Tripel, which both have sort of oblong shapes.
NASA has released a free program called "G.Projector" which can take Equidistant cylindrical maps and reproject them. Doing so will make the distortion you've drawn into your land quite obvious though.
Here are views of the north and south poles from space: "Vertical Perspective" in G.Projector.
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