Trying to represent a spherical object on a flat surface, such that the full sphere can be shown, is a complex problem. In cartography, various map projections have been suggested as the best way to deal with this issue. Regardless of the choice, there will always be a sacrifice in the accuracy of the area, direction, distance, shape, or a combination of these. Thus, each projection comes with advantages and disadvantages, and the debate around choosing one often gets quite personal, with xkcd's Randall Munroe even illustrating the relationship between projection and personality. One way to view where the distortions occur is using Tissot's Indicatrix, in which a mesh and circles are drawn around the sphere, and then studied after various projections.
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