I. World is (approximately) a Sphere
This is the good news and the bad news. On the plus side, there are a lot of simple formulas that apply to a spherical earth. The down side is that we are used to looking at flat pieces of paper. There will always be distortion in making a flat map. The world is large, so if you map only a very small part, this distortion can be made fairly small. For large area maps, of the US, Europe, or the whole world, there will always be significant distortion.
The amount of distortion is dependent on the projection that is used. This is basically the method, algorithm or technique used to put the features from the round earth on the flat map.
A second, and more subtle result of the earth being
a spherical earth is that standard directions, such as north, are not fixed.
What someone in San Francisco says is north is different from someone
in New York or London. The same is true for up, which has more
consequences. Up points outward from the center of the earth (almost).
So it points in a different direction for each point on the earth.
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