You cannot accurately represent the global of the Earth on a flat map. The most common flat map projections grossly overestimate the size of land masses near the poles such as Greenland, Antarctica and Siberia. Recently, Japanese architect Hajime Narukawa came up with an award winning approach to minimize distortion, the AuthaGraph World Map.
As you can see, the map does away with most of the distortion at the poles and gives a better sense of the scale of the Pacific and Indian Oceans. While it emphasizes how far South America is from Asia, it deemphasizes how close it is to Africa. It also makes it easier to visualize the Great Circle airplane routes.
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