There are 2d maps that don’t change the size of objects. The Mercator projection just isn’t one of them.
The Earth is a sphere, and spheres have fundamentally different geometric properties to flat surfaces. So you cannot map a sphere onto a flat plane without distorting *something*. You can change sizes, angles, or other things, but you can’t preserve everything at once. In particular, a map must either distort angles or areas; it cannot preserve both.
The Mercator projection was designed for navigation, because it has the property that lines of constant bearing (that is, you’re always going the same direction on a compass) correspond to straight lines on a Mercator map. Since those are the measurements you usually have on a ship (or had at the time the projection was created), it makes plotting courses easy.
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As for why it distorts sizes: think about how the globe is shaped. There’s a lot more land between 10 N and 20 N than there is between 80 N and 90 N, because the band 10 N to 20 N has to go around the “fat” part of the globe, while the 80-90 N goes around the thin bit near the poles. But the Mercator projection has to make both the same horizontal length to work, which means the 80-90 band gets stretched to be the same size as the 10-20 band.
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