When we make a map, we typically make it on flat paper. We’re mapping a ball, though. The surface of a ball has some different properties than the surface of a flat sheet. For instance, a triangle may have three 90-degree corners on a sphere, but not on paper.
To fit this triangle onto paper, we have to tweak it to fit. So we can be consistent, we need to have a rule for how we tweak things to fit, and that rule will cause some kind of stretching or twisting.
The mercator projection minimizes the stretching near the equator and preserves local angles at the cost of stretching near the poles. The triangle I mentioned earlier would appear as a square on the mercator.
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